The enveloping Lie group A = G x K_e of a connected analytic homogeneous system (G, η) contains a submanifold G x { 1 } which can be identified with G under the canonical imbedding. In this paper, we characterize the class of homogeneous systems imbedded totally geodesically into their enveloping Lie groups, carrying with their canonical connections. It is shown that the class of symmetric homogeneous systems and that of homogeneous systems of Lie groups are essentially the case, among K-semisimple homogeneous systems (Theorem 4).