We describe a perturbative framework in which finite cutoff (Λ) effects can be taken into account. Essentially it consists of keeping terms of O( Λ − 2 ) in the usual perturbation theory once the complete set of dimension-six operators have been included in the Lagrangian with coupling constants proportional to Λ − 2 . This is motivated by Wilson renormalization-group arguments. The occurrence of local gauge anomalies is analyzed within this framework. It is proven that no genuine contribution to the anomaly arises at O( Λ − 2 ). The discussion is completely general though special attention is paid to the standard model.