Insects with gradual or incomplete metamorphosis have three life stages: egg, nymph, and adult. There is no pupal stage as there is in insects with complete metamorphosis, such as butterflies. A nymph usually resembles the adult insect but lacks fully developed wings. In the case of the American cockroach, the female drops her eggs and nymphs hatch from them that resemble the adults, minus the fully developed wings. The nymphs then molt 10-13 times before they reach the adult stage, which takes over a year. American cockroaches can invade kitchens and contaminate food with their their fecal matter and saliva. They also cause an unpleasant smell.

Information from Department of Entomology, Texas A&M University