The bands will strike up. The floats will cruise by. And all over the United States, Labor Day parades will swing into action - just as they always have. But listen carefully amid the roar of Monday's crowds and you may hear an anguished cry. Unionized workers have little to celebrate this Labor Day. Their labor movement is in trouble.
The few bright spots are crystal clear against such a bleak picture. Unions are united - perhaps as never before - in their voter-registration drives aimed at replacing President Reagan with Walter Mondale. The AFL-CIO will even unveil a new theme song, ''Stand With Us, America,'' in an attempt to widen its appeal.
Somehow, though, unions find they are hurting from the dramatic changes in the US economy. Their members are conspicuous exceptions in America's recovery.
The latest bad news comes from the Bureau of National Affairs Inc., a private publishing company specializing in business, economic, and labor news. According to its not-yet-released study, union membership fell below 20 million workers in recession-racked 1982.
That decline is significant, economists say. For if the figures were calculated the same way as previous counts by the US Labor Department, 1982 would be the first time union membership has fallen below 20 million since at least 1968, when the department first published such figures. (The department discontinued its counts after 1980.)
Economists and other union observers are not particularly sanguine about what has happened to labor unions since 1982, either.
''If there is an improvement,'' says one government economist who asked not to be named, ''the evidence is not forthcoming.''
''The picture is brighter only in the sense of how bad things were,'' adds Rudy Oswald, director of AFL-CIO's economic research department. Unemployment is down, but it's still above 1979 levels, he says. And ''many of those (new jobs) are at lower wages.''
The current economic turnaround is what Mr. Oswald calls a ''profits recovery.'' Profits were up 36 percent in the second quarter of 1984 compared with a year ago, he says. Meanwhile, inflation-adjusted compensation for all workers in the private sector was down 0.3 percent.
Why is the labor movement in such a mess?
Because its leaders succeeded in organizing industries with the least growth and the most vulnerability to economic downturns, economists say.
Unions are strong in the goods-producing and governmental sectors of the economy. But the real growth in jobs has been in the private-sector service industries, where unions have had little success in attracting new members.
In 1980, for example, the federal government reported that more than one-third of all workers in construction and manufacturing were represented by labor organizations. Almost a quarter of full-time service employees also had union representation in 1980, but much of that was in government, transportation , and public utilities - sectors that have not grown in recent years.
Job growth has been greatest in industries like trade, finance, insurance, and real estate, where unions do not have a strong foothold.
These long-term changes have been exacerbated by recession, competition from imports, and technological change. Many basic industries - steel and autos, for example - have been hit hard. The dues-paying membership of the United Steelworkers of America, for example, has shrunk by 400,000 workers since 1979.
Other unions, notably the United Automobile Workers (UAW), had to negotiate concessionary contracts with the Big Three automakers. The give-backs helped the companies survive when they were struggling - but also boosted their profits in better times. General Motors (GM) turned in a record $3.7 billion last year.
''Of course we did the right thing,'' UAW president Owen Bieber says of the concessions. ''If we hadn't done the right thing, I don't know where Ford Motor Company would be today.''
But in bargaining this year with GM and Ford, Mr. Bieber says some of the cooperative spirit has vanished. ''There were people on the management side who did take advantage of that cooperative attitude,'' he says. ''I think that's tragic. There is a need for cooperation.''
Of greater concern this year is job security, he says. Joint ventures with foreign automakers and overseas production of cars and parts are threatening American workers. ''If these issues aren't addressed,'' Bieber says, ''in the not-too-distant future, you're looking at a total loss of 1 million jobs in this country.''
Lane Kirkland, president of the AFL-CIO, says job security has become more important in bargaining this year.
Deregulation of certain industries has also put many unions on the defensive.
''The complete and total deregulation of airlines has been a catastrophe in this country,'' says William Winpisinger, head of the International Association of Machinists and Aerospace Workers.
He, too, defends the unions' previous concessions - but as ''quick fixes'' to a difficult situation rather than a long-term move toward more cooperation.
''What (corporations) really mean, in most cases, is that they want labor to unilaterally cooperate,'' he says.
Many unionists say big business is out to bust unions. And neither the National Labor Relations Board nor the White House is lending any help, they add.
That explains in part why union leaders are vitally interested in the 1984 presidential election - and why their voter-registration push is on.
''I see a lot of anti-Reagan (sentiment) here in Rockford,'' says Roosevelt Hood, an Illinois deputy registrar and union member. About 40 percent of the registrars in the area's registration coalition were deputized through labor unions.
The goal is to sign up 30,000 new voters by the Oct. 1 registration cutoff. About 8,000 have been signed up so far.
''We keep looking over our shoulder'' at the deadline, says the director of a local labor community service agency.