Optimal control theory is applied to dynamic operation of batch reverse osmosis (RO) for seawater desalination and batch pressure retarded osmosis (PRO) for power generation. It is proved that the water flux should be constant during the entire operation in order to minimize specific energy consumption (SEC) in RO or to maximize specific energy production (SEP) in PRO. A dimensionless parameter gamma = A(m)L(p)pi(0)t(f)/V-0, similar to that used in continuous osmotic membrane processes, is proposed to characterize the energy performance. While the SEC in RO is a monotonic function of recovery and gamma, the SEP in PRO is solely a monotonic function of gamma. It is shown that batch RO/PRO excels continuous RO/PRO because it mitigates the spatial variation of flux in a long pressure vessel observed in the latter. The batch operation provides an elegant way to implement continuous multistage RO with interstage pumps and an energy recovery device as well as continuous multistage PRO with interstage turbines. Some trade-off between the energy efficiency and flux is deemed necessary. A preliminary cyclic diagram to operate the batch PRO is proposed.