Abstract: An apparatus for hardening cylindrical bearing faces (L) of a shaft (K), wherein at least one of the transitional radii (R1, R2) to the adjoining shaft portions (W1, W2) is constructed recessed, includes a pair of inductive heating units (1, 2), which are each formed at least by one inductor (3, 4) having two spaced-out heating conductor branches (20, 22; 21, 23); an adjusting device (11, 12) for adjusting the inductors (3, 4) simultaneously from the radial direction (R) on to the bearing face (L) to be hardened and a second adjusting device (13, 14) for moving at least the inductor (3, 4) associated with the recessed radius R1, R2) after application to the bearing face (L) by a movement directed axis-parallel with the longitudinal axis (X) of the shaft (K) in the direction of the recessed transitional radius (R1, R2) until its outer heating conductor branch (20) has moved into the particular transitional radius (R1, R2).