In the last ten years we witnessed a rapid development of alternative logical systems, called non-monotonic logics (Baral and Gelfond 1994; Apt and Bol 1994; Minker 1993)--- which allow new axioms to retract existing theorems, and result to be more adequate for common-sense reasoning and modeling dynamic knowledge bases. One of the outcomes of research in the field of non-monotonic logics is represented by the development of a number of languages for knowledge modeling and manipulation. In particular, in the last couple of years a novelprogrammingparadigrn has arisen, called Answer Sets Programming (ASP) (Marek Truszczynski 1999; Niemela to appear), which builds on the mathematical foundations of logic programming and nonmonotonic reasoning. ASP offers novel and highly declarative solutions in a number of well-defined application areas, including intelligent agents, planning, and software modeling and verification. ASP currently benefits from solid and well-developed mathematical foundations, but its programruing aspects still require considerable research. In panicular, there is the need to (1) develop efficient implementations of inference engines for ASP, and (2) develop methodologies for software development in the ASP framework-- i.e., methodologies for representing knowledge using the constructs offered by ASP. Indeed, many of the research teams involved in the development of ASP are currently investing considerable effort in these directions (Cholewinski, Marek, and Truszczynski 1996; Eiter et al. 1998; Niemela and Simons 1997; Lifschitz 1999). The goal of this project is to tackle some of these issues, using constraint solving and parallel processing technology. In particular, in this paper we present some preliminary ideas that have been used to address the first issue--i.e., improving performance of ASP engines--through the use parallelism.