Move over, Mary Poppins: here comes Nanny Inc.:

Mary Poppins has descended on Chicago. More specifically, Beth Smith - Englishwoman, psychologist, professor, divorced mother - has alighted lock, stock, and ''bumbershoot'' at 130 N. Wacker Drive. Her mission, should Americans choose to accept it, is to establish Nanny Inc., the nation's first school for bona fide nannies.

These nannies won't magically ascend the staircase or float over the housetops via umbrella (bumbershoot) like the Julie Andrews incarnation in Walt Disney's movie. They are, in the words of Dr. Smith, ''people motivated and trained to work with children up to age five - and focusing on the emotional, the social, the cognitive, psychological needs of the child, as opposed to a baby-sitter, who takes care of only physical needs.''

High above the Chicago River, this third class of aspirants is making its way through the 400-hour course modeled after - but not limited by - Britain's age-old concept. Nannies are essential, say Smith and co-founder Mary Ellen Gornick, to meet the needs of two-career families and one-parent households spawned by a US society in transition.

''The influx of women into the work force is vastly altering the needs of families left behind,'' says Smith, who has been compared to Julie Andrews but looks more like actress Lynn Redgrave. ''A few years back, career women tended to stay home until their children were four or five, and then they would go back to work when they were in first grade.

''But now women are clearly committed to a career in their own right, want to have children and do it all - even while the kids are young.'' And she says research shows a majority of new mothers would continue to work, even if they had an option not to: ''They feel good about it, find it very self-satisfying. And we have every reason to believe that trend will continue.''

One instructor gently ''burps'' a life-size baby doll bundled against her shoulder just so. And she demonstrates infant-holding techniques: the more reliable two-hand cradle hold and, to free one hand for chores, the one-hand ''football'' hold. Later, she shows students how an infant is properly bathed.

Female students - from older teen-agers to grandmothers, all dressed in pinstriped pinafores - observe, take notes, and take turns doing the burping, bathing, and bundling.

Though no replacement for mom and dad, nannies aim to be the next best thing. A few days at the school and a glance down the curriculum shows you just how much that can entail. There's the basics, of course, like safety and toilet training, bottle feeding, diapering, laundering, regulating of naps and bedtime and nutrition.

But look, too, at the host of current theories on child development: Piaget, Erikson, the Adlerian approach. Enrollees study pre-natal development, heredity vs. environmental influences, how to instill concepts of right and wrong, the ''appropriate'' development of conscience. The list goes on: developing initiative and autonomy, handling anxiety, anger, aggression. It's enough to make you think that if you didn't need a nanny before, you do now.

In one lecture, Amy Peisker, instructor and faculty coordinator, shows how important it is to nurture a child's natural initiative. This can mean not punishing his curiosity in exploring, as well as not avoiding questions. ''When you give a simple, direct answer, it gives the child confidence that he took initiative in the first place,'' she says. ''Rolling your eyes to questions like 'Where does the moon go?' or 'What if the street were made of fudge?' leads to guilt about being curious. Children personalize it.''

Future nannies are taught the difference between infant, toddler, and preschool stages and are tutored extensively in age appropriateness - what activities, toys, and language are suitable for what ages. Besides 8-to-5 classroom work, 143 hours (approximately eight each week) are spent at local ''practicum'' sites - day-care centers, preschools, and children's hospitals. Nannies are given assignments to observe as well as participate with all ages of children.

One assignment: ''Observe two 3-year-olds and two 5-year-olds who are involved in the same activity; . . . make a list of what is similar about the way (they) approach the activity. . . . Do the children work quietly or talk a lot? How do they use the materials? How do they feel about the activity? What behaviors give you clues as to what they are thinking or feeling?'' Ms. Peisker tells the students the idea is to get a feeling for what ''threeness'' and ''fiveness'' are all about.

Back in the classroom, the observations are discussed, and then tips are given on how the nanny's own interaction is directly related to the child's developmental needs. Examples might include how to talk with a child who is shy and withdrawn, how to help him or her puzzle through a task, how to lead several children in discussion, or how to teach them to share toys and equipment.

One of the greatest concerns about those caring for very impressionable youngsters is language. ''It's important not to talk baby talk to infants desperately trying to form the correct sounds,'' Ms. Peisker says. ''And if you are constantly correcting them - 'No, it's ''rabbit,'' not ''wabbit'' ' - you may find that children will stop wanting to communicate.'' She also tells her future nannies that clients will want them to be good and consistent language models - which is very important not only in communication but for future sociability. In all matters - language, sex education, the development of a child's independence - nannies are taught how and when to consult and work with parents.

''Parents worry they might hire a nanny who will know more than they do about how to work with the children,'' Dr. Smith says. ''We help them think through supporting the parents, rather than show themselves off as the expert.''

Dr. Smith was herself a first-time parent at 37. Her frustration in finding good child care for her own 5-year-old put her on the road to Nanny Inc. Her new-mother experience ended up dovetailing nicely with consulting work she was doing. Banks in the area were losing valuable employees, first-time mothers who were having children later in life. The banks called on Smith, then running her own business consulting firm.

''The mothers would try to come back 6 to 12 weeks after having their children, but were not able to handle the job and having a child. One of their consistent concerns was their inability to find good child care. That mirrored my own concern about it.''

The result was Nanny Inc. - a $150,000-plus investment so far. Demographic studies told founders Smith and Gornick that probably only those families in the approximately $250 a week) for a full-time, non-live-in nanny.

''I didn't start this school to be only available to the rich. I wanted to be providing a real service to those who needed it. But it's a dilemma to get the right kind of person in the role. You clearly have to give a salary that's reasonable. Then you start getting very exclusive in terms of who can afford a nanny.''

One answer, she says, is two families that decide to share a nanny. ''If you do that, then you're talking about needing an income of less than $40,000, which includes an awful lot more people that can share costs and benefits.''

Dr. Smith was trained as a nurse in Britain and has a graduate degree in organizational psychology and a PhD in clinical psychology. That, and her experience as a mother, gave her all the necessary ingredients to lead the kind of school she wants, which differs somewhat from similar schools in the country where she was born.

''I wasn't interested in transposing a British curriculum into an American culture. It simply would not have worked. The British (nanny) schools teach needlepoint and social graces and all of that, and clearly that's not transferable to this culture.

''We basically designed our own curriculum on the basis of what we thought should be included and what people ought to know about bringing up children.''

Her first class, of 8 (selected from 200 applicants), graduated in April. A second class, of 6, graduated in June (the class began with 9; 3 were dropped when faculty evaluation found them ''unsuitable''). One graduate, Dorothy Friedlander, had already graduated from one of Britain's two-year nanny programs.

Miss Friedlander says that besides the difference in time investment between the British and American courses, ''the other large difference is education theory and learning how to deal with parents. We didn't learn that in England - and it really seems to broaden your scope about your potential in having a positive effect on a child and family.''

In a short course called ''Nanny: Self as a Person,'' enrollees are taught professional self-esteem and learn how to negotiate a contract with prospective employers. And once they've landed a job, nannies can still keep in touch with the school. A nanny hotline enables them to call faculty about possible household crises. And one evening a month in the year after graduation, they may return to the school for seminars and to compare notes with other job-holding nannies.

Feedback from graduates and clients has convinced Smith that more experience with children is a must. She has increased the practicum-site time by 120 hours and, beginning this summer, will stretch the course over 12 weeks instead of eight. The longer format will ease the intensity of classroom work as well. And Dr. Smith says she is negotiating with universities for 40 hours of college credit for the course.

Besides a stronger emphasis on education theory in this first-ever nanny course in the US, Dr. Smith says the role of the nanny here will differ from the traditional one in Britain.

''Both the children and the nanny were sort of shoved off to the side,'' she says of her home country's model. ''And the nanny would bring them in to say good morning or good night and keep separate from things. We're after a much more integrated process, keeping the nanny as much more a part of the family structure - meals, outings, vacations - as opposed to kind of keeping the children out of the way.''

She says one graduate will have six months' extensive travel with her client family and another has made four trips to Europe since graduation.

Now beginning its third class, Nanny Inc. seems on solid footing. In addition to becoming accredited with the Illinois State Board of Education, the school has gotten extensive coverage in both local and national media, print as well as broadcast. This spring it was awarded $75,000 worth of scholarships by the Comprehensive Employment and Training Act (CETA), enough for about 50 scholarships at $1,500 apiece. The third class has 21 participants. Applicants must have a high school education and documented child-care experience.

Smith began the school with a staff of six and hopes to eventually start franchises elsewhere. ''Many say to us things like: 'This is something I've always wanted to do - work with children. And yet I really haven't found any good way of doing it, and this is the answer to my prayer.' ''

Chicagoan Shelby Boblick hired one of the school's first graduates May 1 and is ''thoroughly pleased'' with the results. She and her husband both work, and recently had their second child (the first is 6). They wanted their children to grow up together in a home environment, but they also knew that most child-care centers wouldn't take two children of such diverse ages anyway.

Besides having bad experiences with live-in help, the Boblicks had sent their first child to day-care centers and to spend time with live-in help at friend's homes. When they had a second child, they wanted better.

''We're delighted in how professionally trained and screened our nanny is,'' says Mrs. Boblick. ''The children are home, happy and it's a whole new and pleasant experience for all of us.''