Constant-pressure molecular-dynamics simulations of phospholipid membranes in the fluid phase reveal strong correlations between equilibrium fluctuations of volume and energy on the nanosecond time-scale. The existence of strong volume-energy correlations was previously deduced indirectly by Heimburg from experiments focusing on the phase transition between the fluid and the ordered gel phases. The correlations, which are reported here for three different membranes (DMPC, DMPS-Na, and DMPSH), have volume-energy correlation coefficients ranging from 0.81 to 0.89. The DMPC membrane was studied at two temperatures showing that the correlation coefficient increases as the phase transition is approached.