Paradigms for using neural networks (NNs) and genetic algorithms (GAs) to heuristieally solve boolean satisfiability (SAT) problems are presented. Results are presented for two-peak and false-peak SAT problems. Since SAT is NP-Complete, any other NP-Complete problem can be transformed into an equivalent SAT problem in polynomial time, and solved via either paradigm. This technique is illustrated for hamiltonian circuit (HC) problems.