Olefinically unsaturated hydrocarbons are prepared from corresponding paraffinic hydrocarbons, in particular propylene is prepared from propane, by dehydrogenation over a catalyst comprising an oxide of a transition metal of group IV B of the Periodic Table, eg. TiO₂ or ZrO₂, and possibly at least one element selected from among elements of transition group VIII, eg. palladium, platinum or rhodium, and/or an element of transition group VI, eg. chromium, molybdenum or tungsten, and/or rhenium and/or tin and possibly a compound of an alkali metal or alkaline earth metal, a compound of main group III or transition group III or zinc.