  Given a grading by an abelian group G on a semisimple Lie algebra L over an
algebraically closed field of characteristic 0, we classify up to isomorphism
the simple objects in the category of finite-dimensional G-graded L-modules.
The invariants appearing in this classification are computed in the case when L
is simple classical (except for type D4, where a partial result is given). In
particular, we obtain criteria to determine when a finite-dimensional simple
L-module admits a G-grading making it a graded L-module.
