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A generalised model of creep deformation in cubic single crystals is developed that considers the combined effects of viscous glide on two (or more) slip systems and accounts for tertiary creep by the accumulation of mobile dislocations with plastic strain. The model is applied to analyse a database of creep curves for the nickel-base single crystal superalloy SRR99 with the assumption that creep deformation occurs by glide on both the {111}< 1 01> and {001}< 110> systems. A procedure for the calculation of creep curves and associated crystal rotations for arbitrary crystal orientations is described. The model predicts changes in the anisotropy of creep behaviour with stress and temperature that is in general agreement with the limited available experimental data. It also includes the contributions of all possible slip vectors to predict crystal rotations that are consistent with observations.