We describe the structure of d-dimensional homogeneous Lorentzian G-manifolds of the form M = G/H of a semisimple Lie group G. Due to a result by N. Kowalsky, it is sufficient to consider the case when the group G acts properly, that is the stabilizer H is compact. Then any homogeneous space G _ H with a smaller group H admits an invariant Lorentzian metric. A homogeneous manifold G/H with a connected compact stabilizer H is called a minimal admissible manifold if it admits an invariant Lorentzian metric, but no homogeneous G-manifold G ~ H with a larger connected compact stabilizer H H admits such a metric. We give a description of minimal homogeneous Lorentzian n-dimensional G-manifolds of the form M = G/H of a simple (compact or noncompact) Lie group G. Let M = G/H be a minimal homogeneous Lorentzian manifolds of a simple noncompact Lie group G. If G has infinite center, then the stabilizer H is a maximal compact subgroup of G. In the case of finite center, the coset space S = G/K by a maximal compact subgroup K is an irreducible Riemannian symmetric space with symmetric decomposition g = k + p. Let H K be a closed subgroup and g = h + m = h + (n + p) the corresponding reductive decomposition, where k = h + n. The subgroup H is admissible if the space m H = n H + p H of Ad H -invariant vectors is nontrivial. We say that the associated admissible manifold M = G/H belongs to the 32.25pt; HEIGHT: 16.5pt" id=_x0000_i1025 type="#_x0000_t75" ?0 and belongs to the 44.25pt; HEIGHT: 16.5pt" id=_x0000_i1025 type="#_x0000_t75" 0. For n ? 11, we obtain a list of all such manifolds M and describe invariant Lorentzian metrics on M.