A set of lines in the photoluminescence spectra of 4H-, 6H-, and 15R-SiC in the near-infrared are attributed to Nb-related defects on the ground of doping experiments conducted with 4H-SiC. A model based on a an exciton bound at the Nb-centre in an asymmetric split vacancy configuration at a hexagonal site is proposed, which explains the structure of the luminescence spectrum and the observed Zeeman splitting of the lines.