EPR and optical (4f-4f photoluminescence and photoluminescence excitation) spectra due to Er centres are studied on bulk ZnSe crystals, which were grown by the high-pressure Bridgman technique and doped with ErF3 (and partly, in addition, with Li2CO3) during crystal growth. Besides the well known, almost isotropic signal with g = 5.94, which has been assigned to isolated Er3+ on Zn lattice sites, we observe three strongly anisotropic EPR spectra (A, B and B') which are due to transitions in non-cubic Er3+ (spectrum A) and Er2+ (spectra B and B') centres. The symmetry axes of these centres have directions close to [111] (A) and parallel to [110] (B and B'). The angular dependences of the signals are influenced by twinning effects. In the crystals doped with ErF3 alone, only a single type of centre, which is obviously identical with the type A EPR centre, manifests itself in photoluminescence. A crystal-field analysis of the corresponding EPR and optical spectra shows that this centre has a Gamma(6)-type ground level and is characterized by a crystal-field parameter ratio A(6)[r(6)]/A(4)[r(4)] = -0.22. We think that this centre is a complex consisting of Er3+ on a Zn site and F on a nearest-neighbour interstitial site. The g-factors found for the EPR signals B and B' can be explained on the basis of non-Kramers doublet ground levels of Er2+ 4f(12) which result from the splitting of cubic Gamma(5) triplets due to non-cubic crystal-field components. These two signals are ascribed to Er2+ on the two zincblende-type interstitial sites, respectively, each forming a complex with some other kind of atom on its next-nearest-neighbour interstitial site. A discussion is given of the result that the EPR spectra (unlike the optical spectra) were detected only in the case of Li2CO3 codoping.