A possibility of intermediately bound excitons in semiconductors doped with transition metal impurities is considered. These sorts of exciton can appear in hexagonal (wurzite-type) semiconductors due to strong hybridization of the conduction band states and the impurity d states. In tetrahedral (zinc blende) semiconductors this hybridization is strongly suppressed due to a symmetry consideration. It is shown that the exciton hole in ZnS:Ni (zinc blende type) is bound by the Coulomb field of the exciton electron and may be considered within the framework of the hydrogen-like model. As for CdS:Ni (wurzite type) the orthogonalization central cell pseudopotential appears to be the leading attracting potential for the hole. These differences in the binding mechanisms account for striking differences measured experimentally in the structure of the exciton spectra and values of the g-factors of these two presumably similar systems.