In this paper we outline a theoretical framework for the combination of decision procedures for the satisfiability of constraints with respect to a constrainttheory. We describe a general combination method which, given a procedure that decides constraint satisfiability with respect to a constraint theory ${\cal T}_1$ and one that decides constraint satisfiability with respect to a constraint theory ${\cal T}_2$, is able to produce a procedure that (semi-)decides constraint satisfiability with respect to the union of ${\cal T}_1$ and ${\cal T}_2$. We also provide some model-theoretic conditions on the constraint language and the component constraint theories for the method to be sound and complete, with special emphasis on the case in which the signatures of ${\cal T}_1$ and ${\cal T}_2$ are non-disjoint.