Pressure versus fluid spacing relations have been obtained for sphingomyelin bilayers in the gel phase and equimolar sphingomyelin/cholesterol in the liquid-crystalline phase by the use of X-ray diffraction analysis of osmotically stressed aqueous dispersions and oriented multilayers. For interbilayer separations in the range of 5-20 A, the repulsive hydration pressure decays exponentially with increasing fluid spacing. The decay length (lambda) of this repulsive pressure is about 2 A for both bovine brain and N-tetracosanoylsphingomyelin, similar to that previously found for phosphatidylcholine bilayers. However, both the magnitude of the hydration pressure and the magnitude of the dipole potential (V) measured for monolayers in equilibrium with liposomes are considerably smaller for sphingomyelin than for either gel or liquid-crystalline phosphatidylcholine bilayers. Addition of equimolar cholesterol increases both the magnitude of the hydration pressure and the dipole potential. These data suggest that the magnitude of the hydration pressure depends on the electric field at the interface as given by (V/lambda)2. For sphingomyelin bilayers, there is a sharp upward break in the pressure-fluid spacing relation at an interbilayer spacing of about 5 A, indicating the onset of steric hindrance between the head groups of apposing bilayers.