Let G be a semi-simple Lie group with finite center and S ⊂ G a semigroup with int S ≠ Ø. A closed subgroup L ⊂ G is said to be S-admissible if S is transitive in G/L. In [10] it was proved that a necessary condition for L to be S-admissible is that its action in B (S) is minimal and contractive where B (S) is the flag manifold associated with S, as in [9]. It is proved here, under an additional assumption, that this condition is also sufficient provided S is a compression semigroup. A subgroup with a finite number of connected components is admissible if and only if its component of the identity is admissible, and if L is a connected admissible group then L is reductive and its semi-simple component E is also admissible. Moreover, E is transitive in B (S) which turns out to be a flag manifold of E. © 1998 Heldermann Verlag.81111128Boothby, W.M., Wilson, E.N., Determination of the transitivity of bilinear systems (1979) SIAM J. on Control Optim., 17, pp. 212-221Barros, C.J.B., San Martin, L.A.B., On the action of semigroups in fiber bundles Mat. Contemp. Bras. Math. Soc., , to appearGuivarc'H, Y., Raugi, A., Frontière de Furstenberg, propriétés de contraction et théorèmes de convergence (1985) Z. Wahrscheinlichkeitstheor. Venv. Geb., 69, pp. 187-242Halmos, P.R., (1960) Lectures on Ergodic Theory, , Chelsea, New YorkLobry, C., Controllability of nonlinear systems on compact manifolds (1974) SIAM J. on Control, 8, pp. 1-4San Martin, L., Crouch, P.E., Controllability on principal fibre bundles with compact structure group (1984) Systems & Control Letters, 5, pp. 35-40San Martin, L., Controllability of families of measure preserving vector fields (1987) Systems & Control Letters, 8, pp. 459-462Invariant control sets on flag manifolds (1993) Math, of Control, Signals and Systems, 6, pp. 41-61San Martin, L.A.B., Tonelli, P.A., Semigroup actions on homogeneous spaces (1995) Semigroup Forum, 50, pp. 59-88Transitive actions of semigroups in semi-simple Lie groups Semigroup Forum, , to appearVaradarajan, V.S., (1974) Lie Groups, Lie Algebras and Their Representations, , Prentice-Hall, Englewood Cliffs, N.JVinberg, E.B., The Morosov-Borel theorem for real Lie groups (1961) Soviet Math. Dokl., 2, pp. 1416-1419Warner, G., (1970) Harmonic Analysis on Semi-simple Lie Groups, I, , Springer-Verlag, Berlin etc