IN 1950, the Nigerian capital of Lagos had a population of 290,000. It was about as big as Wichita, Kan., is today.
But by 2010, greater Lagos is projected to have a population of 21 million - or nearly 1-1/2 times more than metropolitan New York today.
The case of Lagos is more dramatic than most. But it typifies a growth trend, noted in a report issued last week by the United Nations, that has catapulted dozens of the world's small- and medium-sized urban areas into giant megacities within a human lifetime.
Such sudden growth is one reason the world is expected to cross a significant demographic watershed within the next 10 years: For the first time in human history there will be more people living in urban than in rural areas. It is also the main reason for the dramatic spread of urban poverty, which the World Bank predicts "will become the most significant and politically explosive problem in the next century."
The UN report, titled "The Challenge of Urbanization," profiles 100 cities, ranging from Tokyo-Yokohama - with a population of more than 26 million, the world's largest urban agglomeration - to the tiny Fijian capital of Suva, which has a population of 150,000.
Among other things, the report will be a reference for delegates who will gather in June in Istanbul, Turkey, for the second UN Conference on Human Settlements. "Habitat II," as it is known, will address the problem of finding adequate shelter for urban dwellers and developing sustainable living conditions in what the report calls "an urbanizing world."
Just how quickly it is urbanizing is suggested by the fact that by 2000, some 3 billion people may be living in urban areas, three-quarters in developing nations. Another billion - or the equivalent of 60 metropolitan New Yorks - could be added by 2025.
New York itself, the city that in 1950 topped the UN's list of the 10 largest cities, may not even make the list by 2025, as it is overtaken by swelling third-world capitals such as Jakarta and Buenos Aires.
It took London 130 years to climb from 1 million to 8 million residents. Mexico City covered the same distance in just 30 years, between 1940 and 1970, and then doubled again within 16 years.
If UN projections hold true, the combined population of the 10 largest cities at the end of the century - 163 million - will equal that of the 26 smallest countries.
The good news, according to the UN report, is that the rate of urban growth in Asia and Latin America has slowed. The bad news is that huge increments of population are still being added each year, and that Africa - the other main region of the developing world - is continuing rapid urbanization.
About 60 percent of urban growth results from high birth rates in the cities themselves. The balance comes from the huge influx of rural residents pulled into cities by the lure of better jobs and schools and pushed by rural poverty, unemployment, and the exhaustion of agricultural land.
The report says the populations of urban areas in most developing nations will double over the next 10 to 15 years. Such breakneck growth threatens to overwhelm urban governments that have neither the money nor the management and technical skills to keep pace and whose master plans for the future, according to the report, have been overwhelmed by unexpected increases in population.
Poignant evidence that urban governments are failing to keep up can be found in the shantytowns that have cropped up around the periphery of most third-world metropolises, which are cut off from roads, electricity, and clean water. It is also to be found in mountains of uncollected trash, massive traffic congestion, unsafe levels of air pollution, and the estimated 20 million homeless - the equivalent of the combined populations of London and Paris - who wander the urban streets of Latin America alone, reports the World Health Organization.
Fewer than 60 percent of urban dwellers in developing nations have access to sanitation and only 30 percent are connected to sewer systems, according to WHO.
"Throughout the developing world, cities are being inundated in their own wastes as a result of inadequate waste management policies and practices," confirms the UN report.
"It is clearly impossible for these sprawling metropolitan areas - many located in the world's poorest countries - to keep pace with the need for transportation, sanitation, utilities, schools, and hospitals, as long as their populations double every 12 to 20 years," notes a study on urban growth issued by Population Action International, a private advocacy group here.
One way national governments are coping is by decentralizing. In Nigeria, for example, the capital is being moved from overcrowded Lagos to Abuja, in the geographical center of the country.
Other cities are concentrating on more efficient tax-collection to increase the revenues needed to provide additional services. Elsewhere, nations are gravitating toward market economies in an effort to stimulate the economic growth needed to create jobs, wealth, and a larger tax base.
"These will make a difference," says Joseph Chamie, director of the UN's Population Division, publisher of the report. "But not a big enough difference to overcome the enormous challenges third-world cities are facing."