A bearing construction for a crankshaft of a cold Pilger rolling mill for the rolling of tubes wherein the connecting rod is attached to the mill and in which case friction is created between an abrasion bushing made from surface-hardened steel and a bearing box made of high-load or strength synthetic material. For the lubrication of the friction surfaces, the cooling fluid employed for rolling is used. For better removal of heat, the abrasion bushings are provided with means such as cooling fins or similar surface-enlarging profiles and/or materials with high thermal conductivity.