We develop a thermodynamic theory for a difficult class of chemical processes undergoing in irreversible power-producing systems that yield mechanical work and are characterized by multiple (vectorial) efficiencies. Obtained efficiency formulas are applied for chemical machines working at maximum production of power. Steady-state model describes a chemical system in which two reservoirs are infinite. whereas an unsteady model treats a dynamical system with finite upper reservoir and gradually decreasing chemical potential of a key fuel component. In the considered chemical systems total power output is maximized at constraints which take into account dynamics of mass transport and efficiency of power generation. Dynamic optimization methods, in particular variational calculus, lead to optimal functions that describe integral power limits and extend reversible chemical work W-rev to finite rate situations. Optimization results quantify effects of chemical rates and transport phenomena. Legendre transform of a local power function is an effective tool to obtain an optimal path in a dynamical process of power yield. (c) 2008 Elsevier Ltd. All rights reserved.