  In this paper we find conditions which guarantee that a given flow $\Phi$ on
a compact metric space $X$ admits a Lyapunov one-form $\omega$ lying in a
prescribed \v{C}ech cohomology class $\xi\in \check H^1(X;\R)$. These
conditions are formulated in terms of the restriction of $\xi$ to the chain
recurrent set of $\Phi$. The result of the paper may be viewed as a
generalization of a well-known theorem of C. Conley about the existence of
Lyapunov functions.
