The surface morphology of Hg1-xMnxTe epitaxial layers, including HgTe, grown by metalorganic vapour phase epitaxy on GaAs and Cd1-xZnxTe substrates were investigated. The effects of growth temperature, substrate cleaning conditions, composition and orientation on the incidence of hillocks and pits and on general faceting are reported. A simple one-dimensional computer simulation was also developed and used to analyse the observed morphologies. These studies showed that surface morphology was improved by the use of higher temperatures for both substrate cleaning and growth, Mn incorporation, and by increasing the degree of misorientation from {100} towards the {111}B.