A graph G is said to be A:-degenerate whenever every subgraph of G has minimum degree at most A:. A k-degenerate graph G is called maximal k-degenerate if there is no k-degenerate graph H of the same order, which properly contains G. In this paper, we investigate the structure of maximal k-degenerate graphs emphasing to various graph theoretical characteristics and degree constraints. The correspondence between the structure of maximal k-degenerate graphs and the structure of generalized a-critical graphs is characterized.