Irradiation (as in a nuclear reactor) drastically affects the defect structure and its time evolution in a material, and induces new creep mechanisms in it. We present a formalism to evaluate the contribution to creep owing to such mechanisms. Beginning with the phenomenological constitutive relation for the strain appropriate to a given mechanism, we put in simple statistical considerations to derive an expression for the corresponding creep rate. This formal expression is in terms of the defect production rate and a non-equilibrium probability distribution function involving the pertinent properties of the defect type concerned. A convenient approximation scheme for practical calculations is employed, that also makes contact with standard rate theory and provides a proper interpretation for the variables occurring there. As an illustration, we evaluate the contribution to irradiation-induced creep from the orientation-dependent shrinkage of vacancy dislocation loops in an applied stress field. The circumstances inducing transient and non-transient creep are clarified and a numerical estimate is given for the latter component.