The band structure of p-type transparent conducting oxides CuAlO2, CuGaO2, CuInO2 and SrCu2O2 have been calculated by the pseudopotential method within the local density formalism. The band gaps have been found using the B3LYP functional. The minimum indirect gap of CuXO2 decreases along the series X=Al to In, and the valence band maximum is always at the zone boundary. The band maxima of SrCu2O2 are both at Gamma.