Implementing Disequality in a Lazy Functional Logic Language H. Kuchen, F.J. Lopez Fraguas, J.J. Moreno Navarro, M. Rodriguez Artalejo In this paper,we investigate an implementation of a lazy functional logic language (in particular the language BABEL) which uses disequality constraints for solving equations and building answers. We specify a new operational semantics which combines lazy narrowing with disequality constraints and we define an abstract machine tailored to the execution of BABEL programs according to this semantics. The machine is designed as a quite natural extension of a lazy graph narrowing machine. Disjunctions of disequalities are handled using the backtracking mechanism.