To　solve　the　nonlinear　0-1　programming　problem,　it　is　transformed　into　an　equivalent　continuous　nonlinear　programming　on　the　domain　of　[0,　1]　by　a　nonlinear　equality　discrete　constraint.　For　the　0-1　programming　problem　with　nonlinear　object　and　lineav　constraint,　the　problem　with　disorete　constraint　canbe　solved　with　nultiplier　method.　For　the　problem　with　conhinean　object　and　nonlinear　constraint,　the　discrete　constraint　can　be　relaxed　to　a　non-equality　constraint　with　the　constraint　relexing　method.　Both　are　solved　by　the　Genetic　Algorithm　GENOCOP.　The　result　of　multiplier　method　is　more　accurate.　Constraint　relaxing　method　is　an　approximate　method,　can　be　used　to　solve　the　0-1　programming　problem　with　nonlinear　constraint.　Examples　are　presented　and　compared　with　enumerating　method,　and　the　results　show　that　the　approach　is　accurate　and　effective.