Steam accumulators are applied as buffers between steam generators and consumers in cases of different steam production and consumption rates. The application of the steam accumulator saves energy, reduces pressure fluctuations, and prevents aging of tubes and pressurized vessels in steam generators. In this paper, modes of the steam accumulator operation are analyzed and the general design of the steam accumulator control system is defined. Equilibrium and nonequilibrium thermodynamic models of the steam accumulator are presented with the aim of predicting the steam accumulator capacity and as support to the design of the control system. The equilibrium model is based on the mass and energy balance equations of the total water and steam content in the accumulator, while the nonequilibrium model is based on the mass and energy balance equations for each phase and closure laws of nonequilibrium evaporation and condensation rates. The steam accumulator pressure transients are simulated for constant steam charging and discharging flow rates, and the influence of the nonequilibrium condensation and evaporation rates on the steam accumulator capacity is shown. It is concluded that the commonly used equilibrium thermodynamic approach to the steam accumulator design does not provide accurate results in cases of rapid charging and discharging transients; therefore, there is a need for the application of the nonequilibrium approach.