SUMMARYIn this paper, the onset of mechanical instability in time-sensitive elasto-viscoplastic solids is theoretically analyzed at the constitutive level and associated with the occurrence of 'spontaneous accelerations' under stationary external perturbations. For this purpose, a second-order form of Perzyna's constitutive equations is first derived by time differentiation, and a sufficient stability condition is identified for general mixed loading programs. These loading conditions are in fact the most general in both laboratory tests and real boundary value problems, where a combination of certain stress and strain components is known/prescribed.The theoretical analysis leads to find precise stability limits in terms of material hardening modulus. In the case of constitutive relationships with isotropic strain-hardening, no instabilities are possible while the hardening modulus is larger than the so-called 'controllability modulus' defined for (inviscid) elasto-plastic materials. It is also shown that the current stress/strain rate may also directly influence the occurrence of elasto-viscoplastic instability, which is at variance with elasto-plastic inviscid media.