In this paper we report on p-type arsenic doping of CdTe and HgTe/CdTe superlattices by photoassisted and conventional molecular-beam epitaxy (MBE). We also report on some of the problems involved in doping and growing the HgTe/CdTe superlattice system by theoretically examining two key aspects of its growth: (i) growth of CdTe at low temperatures under Cd-stabilized conditions, and (ii) effect of laser excitation on the growing CdTe surface. p-Type arsenic-doped CdTe and HgTe/CdTe superlattice epilayers were grown on (100) CdTe and CdZnTe substrates at low temperatures under cation-stabilized conditions obtained either with excess Cd, or excess Hg fluxes. As-grown arsenic-doped CdTe layers had room temperature carrier concentrations in the 1014–1016 cm−3 range, and hole mobilities of about 35–65 cm2/V s. Low-temperature photoluminescence spectra of arsenic-doped CdTe epilayers grown by photoassisted MBE showed an emission peak at 1.51 eV, which is associated to the AsTe acceptor (arsenic occupying a Te site) with a 92 meV ionization energy. CdTe epilayers grown at low temperatures with photoassisted MBE have superior structural, optical, and electrical properties than those grown by conventional MBE. Arsenic doping of the HgTe/CdTe superlattice structure has resulted in in situ growth of p-type modulation-doped superlattices with enhanced mobilities. Undoped superlattices grown under the same conditions are n-type. These results represent a significant step towards the in situ fabrication of photodiodes and other advanced devices based on HgTe/CdTe doped superlattice structures.