: In this paper we present the concurrent constraint functional programming CCFL and an abstract machine for the evaluation of CCFL programs in a multicore environment. The source language CCFL is a simple lazy functional language with a polymorphic type system augmented by ask-/tell-constraints and conjunctions to express concurrent coordination patterns. As execution model for CCFL we propose the abstract machine ATAF. ATAF implements a G-machine to evaluate functional expressions and provides facilities to run multiple cooperating processes on a fixed set of CPUs. Processes communicate via a shared constraint store realizing residuation semantics and committed choice. We show a few scaling results for parallel programs obtained with a prototypical implementation of ATAF on a quadcore machine.