In this paper three problems are considered: (a) the maximal work that can be produced in a finite time in a thermodynamic system; (b) the minimal work which must be done in order to transform an equilibrium thermodynamic system into a number of subsystems that are out of equilibrium with each other in finite time; and (c) the maximal power that can be achieved in a finite time. The mathematical features of these problems are investigated. It is shown that in many cases the limiting work processes here are processes where intensive variables are piecewise-constant functions of time, and that these functions take not more than some predefined number of values. It is demonstrated that many results obtained for a number of particular systems (heat engines, heat transfer) follow from the general conditions for limiting processes derived in this paper. Conditions for limiting work regimes in mass transfer processes are obtained.