An attempt is made to assess the contributions to the diffuse γ-ray background from normal galaxies, radio galaxies and Seyfert galaxies. Normal galaxies produce about 4 per cent of the background above 100 MeV. Radio galaxies can produce most and perhaps all of the background in the 1–10 MeV range provided their evolution as γ-ray sources is similar to that for their radio properties. Seyfert galaxies will also be important if inverse Compton models are applicable to them, particularly at energies above about 100 MeV.