An elasto-viscoplastic phase field model is proposed to study the microstructural evolutions under mechanical loadings in a Ni-base superalloy single crystal. Elastic anisotropy and inhomogeneity, as well as the description of the long range order in the γ’ phase are included in the model. Plastic activity is introduced using a continuum crystal plasticity framework. The coupled model is used to study microstructural evolutions in superalloys under creep at high temperature. Two loading orientations are investigated,  and . Moreover simulations under alternate fatigue loading in the  orientation are performed. The viscoplasticity simulations are compared to purely elastic phase field simulations and experiments in order to show the influence of plastic activity on microstructural evolutions.