A rolling bearing assembly has an inner race, an outer race and a plurality of rolling elements interposed between respective raceway surfaces of the inner and outer races. A stationary raceway member, which is one of the inner and outer races that are a raceway member and which is non-rotatable, is provided with a stepped face continued with the corresponding raceway surface and located in a direction away from the rolling elements, and is also provided with a gap defining piece having a tip held in face-to-face relation to the stepped face with a gap intervening between it and the stepped face and defining a flow path between a peripheral wall thereof and the stationary raceway member; there being provided a grease reservoir communicated with the flow path.