The invention relates to a process by which C.sub.4- to C.sub.6-olefins or an essentially sulfur-free olefin cut comprising C.sub.4- to C.sub.6-olefins is isomerized over a catalyst comprising an element of the eighth transition group of the Periodic Table, in the presence of at least one added sulfur compound, and any polyunsaturated hydrocarbons contained therein are selectively hydrogenated and hydroisomerized, and also the sulfur compounds are separated from the product and optionally recycled, so that virtually sulfur-free products are obtained.