We consider operators A on a sequentially complete Hausdorff locally convex space X such that - A generates a (sequentially) equicontinuous equibounded C-semigroup. For every Bernstein function f we show that - f(A) generates a semigroup which is of the same ‘kind’ as the one generated by - A. As a special case we obtain that fractional powers - A^α, where α∈ (0 , 1) , are generators.