A procedure for the selective management of the waste of at least part of an automatic machine for manufacturing or packing consumer articles; the procedure comprises the steps of: conveying, according to a first periodic motion law, a plurality of semi-finished articles along a conveying path (CP) through at least one work station (WS), where at least one component (6, 6") is added to an article being processed; feeding, according to a second periodic motion law, each component (6, 6', 6") from a respective store towards the conveying path (CP) and along a feeding path (FP); checking, in a control area (IA) and during the step of feeding the component (6, 6', 6"), the quality and/or the position and/or the orientation of the component itself and establishing whether the component (6, 6', 6") is usable or defective; the method being characterized in that it comprises, in case the component (6, 6', 6") is faulty, a replacement step, during which the defective component is conveyed from the control area (IA) to a waste zone (WZ) and is replaced, inside the work station (WS), by a new component (6"), which is fed from the store towards the conveying path (CP) and along the feeding path (FP); and a compensation step, during which the article being processed is conveyed according to a first modified motion law and the new component (6") is conveyed according to a second modified motion law, thus allowing the new component (6") to reach the work station (WS) so that it can be added to the article being processed; the method comprising a further step, prior to the compensation step, of processing, by means of a control unit and in case the component (6, 6', 6") fed is defective, at least the first modified motion law and/or the second modified motion law based on the current kinematics and/or on the size of the article being processed. conveying, according to a first periodic motion law, a plurality of semi-finished articles along a conveying path (CP) through at least one work station (WS), where at least one component (6, 6") is added to an article being processed; feeding, according to a second periodic motion law, each component (6, 6', 6") from a respective store towards the conveying path (CP) and along a feeding path (FP); checking, in a control area (IA) and during the step of feeding the component (6, 6', 6"), the quality and/or the position and/or the orientation of the component itself and establishing whether the component (6, 6', 6") is usable or defective; the method being characterized in that it comprises, in case the component (6, 6', 6") is faulty, a replacement step, during which the defective component is conveyed from the control area (IA) to a waste zone (WZ) and is replaced, inside the work station (WS), by a new component (6"), which is fed from the store towards the conveying path (CP) and along the feeding path (FP); and a compensation step, during which the article being processed is conveyed according to a first modified motion law and the new component (6") is conveyed according to a second modified motion law, thus allowing the new component (6") to reach the work station (WS) so that it can be added to the article being processed; the method comprising a further step, prior to the compensation step, of processing, by means of a control unit and in case the component (6, 6', 6") fed is defective, at least the first modified motion law and/or the second modified motion law based on the current kinematics and/or on the size of the article being processed. <EOS>