A billet is rolled in a rolling mill into a first process section in a succession of roll stands arranged along a first pass line. The first process section is either delivered as a finished product to a cooling bed or alternatively slit into second and third process sections which are subjected respectively to additional rolling in finishing blocks arranged on second and third pass lines parallel to the first pass line. At least one of the finishing blocks is shiftable onto the first pass line in order to subject the first process section to additional rolling prior to delivering it to the cooling bed.