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For the purpose of good reproduction and prediction of creep deformation of nickel-base single crystal superalloys at intermediate temperatures, a phenomenological creep model is developed, which accounts for the typical γ/γ′ microstructure and the individual thermally activated elementary deformation processes in different phases. The internal stresses from γ/γ′ lattice mismatch and deformation heterogeneity are introduced through an efficient method. The strain hardening, the Orowan stress, the softening effect due to dislocation climb along γ/γ′ interfaces and the formation of ⟨112⟩ dislocation ribbons, and the Kear–Wilsdorf-lock effect as key factors in the main flow rules are formulated properly. By taking the cube slip in ⟨110⟩{100} slip systems and ⟨112⟩{111} twinning mechanisms into account, the creep behavior for [110] and [111] loading directions are well captured. Without specific interaction and evolution of dislocations, the simulations of this model achieve a good agreement with experimental creep results and reproduce temperature, stress and crystallographic orientation dependences. It can also be used as the constitutive relation at material points in finite element calculations with complex boundary conditions in various components of superalloys to predict creep behavior and local stress distributions.