For both finite and infinite thermal capacitance rates of heat reservoirs, the finite-time thermodynamic performance of steady flow Carnot and Brayton heat pump cycles has been studied. The fundamental optimal relations of the two cycles are obtained. The performance characteristics of the two cycles for the same boundary conditions are compared. The effects of finite thermal capacitance rates of the working fluid and heat reservoirs and of the internal irreversibilities of the cycles on cycle performance are analysed. Optimal matching between the temperatures of the working fluid and heat reservoirs is discussed.