We report p-type doping of tellurium-based compounds (CdTe, ZnTe) and alloys (CdMgTe, ZnMgTe, ZnCdTe) in molecular beam epitaxy using nitrogen atoms from a plasma source. The dominant shallow acceptor, as deduced from transport and optical measurements, has an ionization energy close to the effective mass value. A systematic decrease of the doping efficiency is observed as the Zn content decreases. We discuss the key role of the Zn content in the material in the framework of two factors: (i) local strain induced in the lattice by the presence of nitrogen and (ii) formation of compounds involving nitrogen atoms.