Author’s abstract: “The Clark-Haussmann formula, giving the integrand in the stochastic integral representation of a functional L(\({\mathcal H}(w))\), where \({\mathcal H}=(x_ t)_{t\in [0,T]}\) is a diffusion process in \({\mathbb{R}}^ n\) and L is a mapping from \(C([0,T],{\mathbb{R}}^ n)\) to \({\mathbb{R}}\), is equivalent to a computation of the Wiener space derivative of the functional \(w\to L({\mathcal H}(w))\). It involves the Fréchet derivative of L. Here we are concerned with the case of diffusions on a manifold M and with a functional L: C([0,T],M)\(\to {\mathbb{R}}\); now the Fréchet derivative is no longer available. We show that a similar formula can be obtained involving a family of scalar measures \(v_ x\) and 1-forms \(q_ x(t)\) associated with L. The proof uses stochastic flow theory and the manifold structure of the space C([0,T],M).”