For at least the past decade they have been moving upstream at the rate of 50 miles a year. Now they are no more than 25 miles away from wrecking the ecosystem of North America's largest water system.
Fisheries experts in Chicago are battling to keep thousands of huge Asian carp from entering Lake Michigan and the rest of the Great Lakes. The fat, voracious fish that escaped into the Mississippi River from ponds hundreds of miles away are now within the city limits.
"They could wipe out the base of the food chain in the entire Great Lakes," said Dennis Schornack, US chairman of the International Joint Commission, which oversees the water systems affecting the US and Canada. "We could end up with a situation where the Great Lakes are nothing more than a carp pond."
The carp, native to the Far East, were introduced in Arkansas in the early 1970s to act as algae eaters by the catfish-farming industry. But many escaped as a result of floods, entering tributaries of the Mississippi and heading north in search of cooler water.
By the time the carp reach maturity they can be more than five feet long and weigh 110lb.Their size and appetite mean they are not only a threat to the food system – but also a physical threat to people. There are numerous stories of fishermen being struck by the leaping fish. One suffered a broken nose.
If man had not tinkered with the river system, the carp would not be threatening the Great Lakes. The Chicago river, which runs through the city, never had any link with the Mississippi and flowed in the opposite direction, into Lake Michigan.
But in the 19th century the river was used as a dumping ground for sewage and slaughterhouse waste and concern grew that Lake Michigan, which provided the city's water, would be polluted. So engineers built a series of canals linking the river with the Illinois River, which flows into the Mississippi basin, and reversed the Chicago River's flow.
Experts are resorting to radical methods to try to prevent the fish from entering the lake. Since April, the Army engineers have been using an electrical current to try to deter the fish.
"It is highly unlikely that it would be able to remove them from the Mississippi basin," said Mr Schornack. "That is the problem with foreign species. Once they are established it is very hard to get rid of them."