The regulation of insect respiratory gas exchange has long been an area of interest. In particular, the reason why insects from at least five orders exhibit patterns of gas exchange that include regular periods of spiracular closure has been the source of much controversy. Three adaptive hypotheses propose that these discontinuous gas-exchange cycles (DGCs) evolved to either limit water loss across respiratory surfaces, facilitate gas exchange in underground environments or to limit oxidative damage. It is possible that DGCs evolved independently multiple times and for different reasons, but for DGCs to be a plausible target for natural selection, they must be heritable and confer a fitness benefit. In a previous study of cockroaches Nauphoeta cinerea, we demonstrated that DGCs are repeatable and extend survival under food and water restriction. Here, we show for the first time that DGCs are heritable, suggesting that they are a plausible target for natural selection.