The work of \textit{L. Bérard-Bergery} and \textit{J.-P. Bourguignon} [Lect. Notes Math. 838, 30-35 (1981; Zbl 0437.53030)] on the Laplace-Beltrami operator acting on functions defined on the total space of a Riemannian submersion with totally geodesic fibers is extended to totally geodesic, bundle-like foliations \({\mathcal F}\) on a compact Riemannian manifold. In this case, there exist, apart from the Laplacian associated to the metric, natural differential operators \(\Delta_{\mathcal F}\) and \(\Delta_{\mathcal T}\), called vertical and horizontal Laplacians, respectively, and the authors investigate their commutation properties.