"This is a previously unrealised challenge in cockroaches," Purdue University professor Michael Scharf said.
"Cockroaches developing resistance to multiple classes of insecticides at once will make controlling these pests almost impossible with chemicals alone."
The team tested different insecticides from different classes, and combinations, in Indiana and Illinois over a six-month period.
Exterminators often combine insecticides to produce the most likely lethal dose to the cockroches. The scientists tried to do the same but were surprised by the resistence in most cases.
"If you have the ability to test the roaches first and pick and insecticide that has low resistance, that ups the odds," Scharf said.
"But even then, we had trouble controlling populations."
The team said it could not make a dent in the population that remained largely static.
With a two-insecticide mixture, the pests appeared to thrive.
"We would see resistance increase four- or six-fold in just one generation," Scharf said.
"We didn't have a clue that something like that could happen this fast.
"Some of these methods are more expensive than using only insecticides, but if those insecticides aren't going to control or eliminate a population, you're just throwing money away," Scharf said.
"Combining several methods will be the most effective way to eliminate cockroaches."
Why are cockroches so hard to kill
The American cockroach (Periplaneta americana) is an omnivorous scavenger and one of the largest insect species that lives in close proximity to humans.
It has one of the largest genomes known to exist among insects, second only to the common locust.
In total, the species has 20,000 genes - which is the same number as a human.
Some genes control its internal detoxification system, which means the cockroach doesn't get ill if it eats toxic food.
More genes help it combat infections, meaning it is resilient to living in filthy conditions.
Cockroaches can also regrow limbs thank to its remarkable genetic sequence.
Scientists have also found that female cockroaches are so resilient they don't need a male partner. - Daily Mail