Relative permeability hysteresis has been measured for a water-wet outcrop rock sample and a mixed-wet reservoir core. For the oil phase, imbibition and drainage relative permeability curves differed significantly. The difference was much less pronounced for the water phase. Scanning curves, which characterize transitions between imbibition and drainage curves, were also measured. A notable characteristic of the oil relative permeability scanning curves is their reversibility; along most of the length of a scanning curve, oil relative permeability exhibits no hysteresis. A proposed mechanism for the reversible behavior is pinning of water/oil interfaces on surfaces of rock grains. Pinned interfaces remain anchored at fixed positions on grains despite changes in interface curvature and contact angle. In water-wet samples, pinning can occur as a result of contact-angle hysteresis. In mixed-wet rock, pinning can occur at the boundaries between water- and oil-wet grain surfaces. As long as interfaces remain pinned, pore-level fluid geometry is a function of saturation only and does not depend on the direction of saturation change.