This　paper　is　concerned　with　the　asymptotic　stability　of　travelling　wave　front　solutions　with　algebraic　decay　for　n-degree　Fisher-type　equations.　By　detailed　spectral　analysis,　each　travelling　wave　front　solution　with　non-critical　speed　is　proved　to　be　locally　exponentially　stable　to　perturbations　in　some　exponentially　weighted　L-infinity　spaces.　Further　by　Evans　function　method　and　detailed　semigroup　estimates,　the　travelling　wave　fronts　with　non-critical　speed　are　proved　to　be　locally　algebraically　stable　to　perturbations　in　some　polynomially　weighted　L-infinity　spaces.　It＇s　remarked　that　due　to　the　slow　algebraic　decay　rate　of　the　wave　at　+infinity,　the　Evans　function　constructed　in　this　paper　is　an　extension　of　the　definitions　in　[1,　3,　7,　11,　21]　to　some　extent,　and　the　Evans　function　can　be　extended　analytically　in　the　neighborhood　of　the　origin.