Abstract: C.sub.4 -C.sub.6 -alkenes having an internal double bond can be produced by hydroisomerization of C.sub.4 -C.sub.6 -alkenes having a terminal double bond in the presence of H.sub.2 on a catalyst having a content of a noble metal of group VIII of the Periodic Table of the Elements (Mendeleev), if C.sub.4 -C.sub.6 -alkenes having a terminal double bond are fed into a hydroisomerization reactor after preheating, as such or in a mixture with other hydrocarbons, and the reaction product is divided into a work-up stream and a recycle stream. The recycle stream is recycled to the inlet of the hydroisomerization reactor and is used there as feed together with the C.sub.4 -C.sub.6 -alkenes having a terminal double bond or with the hydrocarbon stream comprising the C.sub.4 -C.sub.6 -alkenes having a terminal double bond and with the H.sub.2.