To provide a rolling bearing assembly, in which a grease filled within the bearing assembly is utilized to achieve a high speed feature, a long life and a maintenance-free and a lubricant oil can be stably supplied from a minute gap, a stepped face continued from the raceway surface is provided in a stationary raceway ring unit of an inner and outer ring units in a direction away from rolling elements. A gap forming piece having a free end confronting the stepped face is provided to define therebetween a flow passage and a grease reservoir communicated with the flow passage. The rolling bearing assembly is so designed that a heat cycle can be induced in the grease reservoir and, base oil of the grease can be urged to flow out from the gap by the effect of a pressure variation caused by the temperature rise.