Constitutive equations are constructed for single-crystal nickel-based superalloys. Account is taken of dislocation glide in the channels of the matrix phase (referred to as c) of the face-centred cubic (fcc) type, dislocation climb at the interfaces with the reinforcing L1 2 precipitates (referred to as c 0 ) and the processes leading to cutting of the interfaces by dislocation ribbons via stacking fault shear of the ah1 1 2i type. A treatment of ah1 1 2i ribbons produced by the combination of a=2h1 1 0i channel dislocations by an appropriate set of dislocation reactions is developed. The model allows the following features of superalloy creep to be recovered: dependence upon microstructure and its scale, effect of lattice misfit, internal stress relaxation, incubation phenomena, the interrelationship of tertiary and primary creep, and vacancy condensation leading to damage accumulation. Using the model, the creep deformation behaviour of the singlecrystal superalloy CMSX-4 is studied, with emphasis on the interrelationship between primary and tertiary creep. It is shown that the values for the various parameters used in the modelling are physically reasonable and are related to the microstructure and its evolution during creep. The creep anisotropy prevalent in these materials due to primary creep is recovered correctly.