An elementary argument is used to show that the Markov semigroup of a stochastic dynamical system which has a flow consisting of diffeomorphisms necessarily preserves the space of continuous functions vanishing at infinity. In the one dimensional case this is seen to be also a sufficient condition. As a corollary there is a result proved by Kunita under slightly stronger conditions on the coefficients: a non-degenerate system on R has a flow consisting of homeomorphisms if and only if both ± ∞ are natural boundaries.