Creep is a serious concern reducing the efficiency and service life of components in various structural applications. Multi-principal element alloys are attractive as a new generation of structural materials due to their desirable elevated temperature mechanical properties. Here, time-dependent plastic deformation behavior of two multi-principal element alloys, CoCrNi and CoCrFeMnNi, was investigated using nano-indentation technique over the temperature range of 298 K to 573 K under static and dynamic loads with applied load up to 1000 mN. The stress exponent was determined to be in the range of 15 to 135 indicating dislocation creep as the dominant mechanism. The activation volume was ~25b3 for both CoCrNi and CoCrFeMnNi alloys, which is in the range indicating dislocation glide. The stress exponent increased with increasing indentation depth due to higher density and entanglement of dislocations, and decreased with increasing temperature owing to thermally activated dislocations. The results for the two multi-principal element alloys were compared with pure Ni. CoCrNi showed the smallest creep displacement and the highest activation energy among the three systems studied indicating its superior creep resistance.