  We study the extensibility problem of a pair of derivations associated with
an abelian extension of algebras with bracket, and derive an exact sequence of
the Wells type. We introduce crossed modules for algebras with bracket and
prove their equivalence with internal categories in the category of algebras
with bracket. We interpret the set of equivalence classes of crossed extensions
as the second cohomology. Finally, we construct an eight term exact sequence in
the cohomology of algebras with bracket.
