The concept of availability as an upper bound to the work that can be extracted from a given system in connection with specified surroundings is extended to processes constrained to operate at nonzero rates or in finite times. Such analyses are facilitated by the introduction of generic models which describe a whole range of systems in such a way that the optimal performance of the generic model is an upper bound to the performance of the real systems. The effects of the time constraint are explored in general and in more detail for a generic model in which extraction of work competes with internal relaxation. Extensions to nonmechanical systems are indicated. We hereby wish to establish the finite-time availability as a standard of performance more useful than the traditional availability based on reversible processes.