A crystal viscoplasticity (CVP) model for the creep-fatigue interactions of nickel-base superalloy CMSX-8 is proposed. At the microstructure scale of relevance, the superalloys are a composite material comprised of a γ phase and a γ′ strengthening phase with unique deformation mechanisms that are highly dependent on temperature. Considering the differences in the deformation of the individual material phases is paramount to predicting the deformation behavior of superalloys at a wide range of temperatures. In this work, we account for the relevant deformation mechanisms that take place in both material phases by utilizing two additive strain rates to model the deformation on each material phase. The model is capable of representing the creep-fatigue interactions in single-crystal superalloys for realistic 3-dimensional components in an Abaqus User Material Subroutine (UMAT). Using a set of material parameters calibrated to superalloy CMSX-8, the model predicts creep-fatigue, fatigue and thermomechanical fatigue behavior of this single-crystal superalloy. Finally, a sensitivity study of the material parameters is done to explore the effect on the deformation due to changes in the material parameters relevant to the microstructure. •The crystal viscoplasticity model explicitly models the deformation in the gamma and gamma' phases.•The model predicts creep-fatigue and thermomechanical fatigue responses.•The full 3D model is implemented as a user subroutine for ABAQUS.•Parameters are established for a reduced Re single-crystal Ni-base superalloy.