If A and G are separable locally
compact topological groups with A abelian, a central group extension Gf, itself a
separable locally compact topological group, of A by G can be defined for each
Bore12-cocycle f from G to A. The structure of the group algebras of Gf has been
studied for the case of compact A. In this paper stmcture theorems for these group
algebras are obtained in the general situation.