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In this paper, we present results on the first MBE growth of HgSe. The influence of the GaAs substrate temperature as well as the Hg and Se fluxes on the growth and the electrical properties has been investigated. It has been found that the growth rate is very low at substrate temperatures above 120°C. At 120°C and at lower temperatures, the growth rate is appreciably higher. The sticking coefficient of Se seems to depend inversely on the Hg/Se flux ratio. Epitaxial growth could be maintained at 70°C with Hg/Se flux ratios between lOO and ISO, and at 160°C between 280 and 450. The electron mobilities of these HgSe epilayers at room temperature decrease from a maximum value of 8.2 x 10^3 cm2 /V' s with increasing electron concentration. The concentration was found to be between 6xlO^17 and 1.6x10^19 cm- 3 at room temperature. Rocking curves from X-ray diffraction measurements of the better epilayers have a full width at half maximum of 5S0 arc sec.