The invention relates to a cosmetic composition that contains at least one poly-alpha-olefin which is obtained by subjecting, at a temperature in the range of from 60° to 340 °C, at least one primary alcohol to a dehydration polymerization in the presence of an acidic alumino phyllosilicate. The primary alcohol is selected from the group of unsaturated monofunctional alcohols, branched monofunctional alcohols and difunctional alcohols. The cosmetic composition may also contain the corresponding hydrated poly-alpha-olefins. The invention also relates to the use of the hydrated or non-hydrated poly-alpha-olefins as oil bodies in cosmetic or pharmaceutical preparations.
