ABSTRACT. Extending ASP with constraints (CASP) enhances its expressiveness and performance. This extension is not straightforward as the grounding phase, present in most ASP systems, removes variables and the links among them, and also causes a combinatorial explosion in the size of the program. This has led CASP systems to devise several methods to overcome this issue: restricting the constraint domains (e.g., discrete instead of dense), where constraints can appear, or the type (or number) of models that can be returned. In this paper we propose to incorporate constraints into s(ASP), a goal-directed, top-down execution model which implements ASP while retaining logical variables both during execution and in the answer sets. The resulting model, s(CASP), can constrain variables that (as in CLP) are kept during the execution and in the answer sets. s(CASP) inherits and generalizes the execution model of s(ASP) while parameterizing the constraint solver. We describe this novel execution model and show, through several examples, the enhanced expressiveness of s(CASP) w.r.t. ASP, CLP, and other ASP systems with constraints. We also report improved performance w.r.t. other very mature, highly optimized ASP systems in some benchmarks.