About 6:30 weekday mornings, throngs of bicycles, with a smattering of motor scooters and pedestrians, pour off the ferries that carry bikers and other passengers free of charge across the IJ (pronounced “eye”) harbor, clogging the streets and causing traffic jams down behind Amsterdam’s main train station. “In the afternoon it’s even more,” moaned Erwin Schoof, a metalworker in his 20s who lives in the canal-laced center of town and battles the chaos daily to cross to his job. Willem van Heijningen, a railway official responsible for bikes around the station, said, “It’s not a war zone, but it’s the next thing to it.” This clogged stream of cyclists is just one of many in a city as renowned for bikes as Los Angeles is for automobiles or Venice for gondolas. Cyclists young and old pedal through narrow lanes and along canals. Mothers and fathers balance toddlers in spacious wooden boxes affixed to their bikes, ferrying them to school or day care. Carpenters carry tools and supplies in similar contraptions and electricians their cables. Few wear helmets. Increasingly, some are saying what was simply unthinkable just a few years ago: There are too many bikes. While cities like New York struggle to get people onto bikes, Amsterdam is trying to keep its hordes of bikes under control. In a city of 800,000, there are 880,000 bicycles, the government estimates, four times the number of cars. In the past two decades, travel by bike has grown by 40 percent so that now about 32 percent of all trips within the city are by bike, compared with 22 percent by car. Applauding this accomplishment, a Danish urban planning consultancy, Copenhagenize Design, which publishes an annual list of the 20 most bike-friendly cities, placed Amsterdam in first place this year, as it has frequently in the past. (The list consists mostly of European cities, though Tokyo; Nagoya, Japan; and Rio de Janeiro made the cut. Montreal is the only North American city included.) But many Amsterdamers say it is not so much the traffic jams like those at the morning ferry that annoy them most, but the problem of where to park their bikes once they get to where they’re going, in a city with almost more water than paved surfaces. “Just look at this place!” said Xem Smit, 22, who for the past year has struggled to maintain order at a municipal bike parking lot in the heart of town, waving a hand at bikes chained to lampposts, benches, trees and almost any other permanent object across a tree-lined square between the stock market and the big De Bijenkorf department store. “I hear complaints all the time,” Mr. Smit said. “It’s not bike friendly — no!” His tiny, fenced-in parking lot has space officially for 140 bikes, but he routinely crams in more. “My record is 152,” he said. Mr. Smit’s problem is largely what keeps Thomas Koorn, of Amsterdam’s Transport and Traffic Department, awake at night. “We have a real parking issue,” he said in a conference room overlooking the IJ. Over the next two decades, Mr. Koorn said, the city will invest $135 million to improve the biking infrastructure, including the creation of 38,000 bike parking racks “in the hot spots.” “We don’t think there’s a crisis; we want to keep it attractive,” Mr. Koorn said. He paused, then added, “You cannot imagine if all this traffic were cars.” Part of the problem is that many Amsterdamers are not satisfied with just one bike, and often do not care where they leave those they have. “I have three,” said Timo Klein, 23, an economics student, picking one of his out from a scattering of dozens of bikes on the central Dam Square, some still usable, others clearly wrecks. “If one breaks down, I don’t have to use public transportation,” like buses or trams, which in the city’s narrow, clogged roadways are slower than bikes. With so many bikes around, one of the more powerful lobbies in town is the Fietsersbond, or Cyclists’ Union, with its 4,000 local members. Musing over why Amsterdamers are so keen on bikes, Michèl Post, a union official, attributed it to the country’s density.