Abstract: The rolling/sliding outer ring of the cam follower apparatus withstand peeling very well, even in sever lubrication conditions, through the steps that on the outer peripheral surface of the outer ring, the depth of the surface layer is taken to be 0 to 50 .mu.m, and the maximum residual compressive stress in this surface layer is between 50 and 110 kgf/mm.sup.2, the hardness of this surface layer is between Hv830 and Hv960, and the average wavelength of the very minute protrusions on the surface is less than 25 .mu.m, and the amount of residual austenite in the surface layer exceeds 7 volume %, after processing, while the inner peripheral surface, of the outer ring is superfinished.