This thesis is devoted to the study of some kind of Backward Stochastic Differential Equations (BSDE for short) with a drift f, whose solutions belong to a Riemannian manifold with connection. It generalizes two well-known problems: the research for martingales with prescribed terminal value, and the existence and uniqueness of solutions to euclidean BSDE with Lipschitz drift, originally studied by E. Pardoux and S. Peng.