In this study, the TMF stress relaxation and creep behavior at 1023 K and 1223 K (750 °C and 950 °C) have been investigated for a Ni-based single-crystal superalloy. Specimens with three different crystal orientations along their axes were tested; <001>, <011>, and <111>, respectively. A highly anisotropic behavior during TMF stress relaxation was found where the <111> direction significantly shows the worst properties of all directions. The TMF stress relaxation tests were performed in both tension and compression and the results indicate a clear tension/compression asymmetry for all directions where the greatest asymmetry was observed for the <001> direction at 1023 K (750 °C); here the creep rate was ten times higher in compression than tension. This study also shows that TMF cycling seems to influence the creep rate during stress relaxation temporarily, but after some time it decreases again and adapts to the pre-unloading creep rate. Creep rates from the TMF stress relaxation tests are also compared to conventional constant load creep rates and a good agreement is found.