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Time-dependent rock deformation affects both natural processes happening on the geological time scale and subsurface engineering operations. We perform a series of multistage triaxial experiments on a set of natural limestone and artificial samples. We study rock response during creep and stress relaxation tests, which are two endmembers of time-dependent rock response. The tests were conducted at room temperature and low confining pressure. We find that all rock samples showed pronounced creep and stress relaxation both at low-stress levels corresponding to half of the yield stress and higher stresses corresponding to yield stress. Associated values of bulk and shear viscosities lie in the range of 1015–1017 Pa s for artificial and 1015–1016 Pa s for limestone samples at critical stresses corresponding to failure limits. At low stresses, effective viscosities are significantly higher. Bulk viscosity is up to two times higher than shear viscosity. Viscosity values correlate well with failure properties. Samples with low strength show the lowest values of viscosities. All samples exhibited significant dilation during creep experiments, which was not associated with the formation of the macroscale fracture or strain localization. Creep and stress relaxation tests show different stress–strain rate behavior. [ABSTRACT FROM AUTHOR]