This paper is concerned with a theory of viscoelastic/plastic solids which reduces to that of the classical (linear) viscoelasticity as one limiting case and to the (inviscid) theory of elastic/plastic solids in another. Whereas the viscoelastic strain rates are assumed to be derivable from the appropriate creep integral laws of classical viscoelasticity, the plastic strain rates in stress space are dependent not only on the path history but also the time history of stress. After postulating the existence of a regular loading surface in the viscoelastic-plastic state and deducing the appropriate criterion for loading, a major portion of the paper is devoted to establishing (a) the convexity of the loading surface, (b) the direction of the plastic strain-rate vector in stress space, and (c) the structure of the constitutive equations for the plastic strain rates. The loading surface of the present theory (in contrast to that of the inviscid theory of plasticity), being dependent on certain measures representing time history of stress, is allowed to change its shape continually; this has implications in the interpretation of experimental results dealing with the determination of the initial and subsequent yield surfaces where corners are observed.