In a previous paper a minimum principle has been formulated for the solution of the rate problem in elastic-perfectly plastic solids with regular yield surface. In this paper such a principle is extended to work-hardening materials with regular yield surface. The generalisation of the principle for singular yield surfaces, both for elastic-perfectly plastic and for elastic-work-hardening materials, in also given. Finally it is shown that such principles are intimately related to a recent theorem due to Ceradini.