Asked by Jonny Osmond
This depends on the species. In the case of the cosmopolitan pest species that breeds indoors, like American and German cockroaches, both sexes have well-developed wings and are able to ﬂy. Male oriental cockroaches, however, have wings reduced in length and the females just have small buds, so neither sex can ﬂy. Some tropical species like the giant hissing cockroach from Madagascar are wingless in both males and females. In Britain we have three species of native cockroach all of which have well-developed wings, and so are capable of ﬂight.
Phil Rispin, Curatorial assistant of Etymology at The Manchester Museum