The good high temperature strength of Ni-base single crystal superalloys (SX) qualifies them for blade applications in gas turbines in aero engines and power plants. Turbine blades have to withstand a load spectrum, which involves creep and fatigue components. In laboratory tests, high temperature strength of SX is assessed using constant strain rate (CSR), creep and anisothermal out-of-phase thermomechanical fatigue (TMF) testing. In the present work we compare these three types of tests in the temperature range between 1023 and 1223 K, for one superalloy of CMSX-4 type. We perform isothermal CSR and creep tests in this temperature range. Anisothermal out-of-phase TMF tests are performed using these two temperatures as minimum and maximum temperatures (T_min and T_max) in the tension/compression part of the cycle, respectively. Precisely oriented [001]-specimens are used, which allows to exclude experimental scatter associated with variations in specimen orientations. Emphasis is placed on analyzing how high temperature plasticity manifests itself in these three types of tests, which are all affected by elementary micro creep processes. Several interesting results are obtained. While an increase of yield stress with temperature during CSR testing (material strength increases) is observed, creep rates decrease with increasing temperature (which represents softening). It was also found that when the creep element of a TMF cycle is promoted (by extending the period of the compression heating part of the cycle), TMF lives decrease. Surface quality which has a strong effect on TMF does not significantly affect creep behavior. The three types of tests are associated with different deformation/damage mechanisms. Creep represents a homogeneous deformation with internal damage evolution while fatigue is associated with localized deformation and oxidation assisted crack initiation and growth starting at the specimen surface. The results are discussed in the light of previous results published in the literature.