AbstractBand structure calculations are carried out for hypothetical nonmagnetic alloys Co2Ga and Co2MnGa and for the ferromagnetic alloy Co2MnGa, all with the L21structure. The results are used to investigate the electrical conductivity of (Co, Ga) and Co(Ga, TM) alloys (where TM is a transition metal), particularly as this involves hopping conduction. Explanation of the latter by the presence of antistructure Co or TM atoms on the Ga subslattice seems to be confirmed although they do not affect normal conduction appreciably. Mn assists hopping conduction less than antistructure Co since it provides fewer good hopping states, albeit better ones.