Let u: G —> A be a differentiable representation of a Lie group into a 6-algebra. The differential u0 = du, of u at the neutral element e of G is a representation of the Lie algebra 9 of G into A. Because a Lie group is locally the union of one-parameter subgroups and since the infinitesimal generator of a differentiable (multiplicative) sub-semi-group of A determines this sub-semi-group, the representation u0 determines u if G is connected. We shall be concerned wi h the converse: given a representation u0 of o, when can it be obtained by differentiating a representation u of G? We shall assume G connected and simply connected, which means that we are only interested in the local aspect of the problem.