1. A method for monitoring the quality of laser-machining processes ( 500 ), in particular laser-cutting or laser-welding processes, including the operations of: acquiring via sensor means ( 540 ), in particular optical sensors, a machining-process signal (Xp) and calculating from said signal representing the process (Xp) parameters (E 1 , E 2 , DC) representing the machining quality during the laser-machining process; and making available ( 130 ) corresponding reference parameters (E 1 r , E 2 r , DCr) representing a given machining quality, calculated from a process reference signal (Xr) acquired via said sensor means ( 540 ), said method being characterized in that it further includes the operations of: comparing ( 230 ) said parameters (E 1 , E 2 , DC) representing the machining quality with said reference parameters (E 1 r , E 2 r , DCr) representing a given machining quality to obtain a set of regulated process parameters (N 1 , N 2 , NDC); making available ( 140 ) a plurality of statistical models (θ k ) that identify respective states of the machining process ( 500 ), said states including states of defect (D); and executing in real time an operation of recognition ( 300 ) of membership for a set of process observations (x; N 1 , N 2 , NDC, DIR) acquired in real time which includes said set of regulated process parameters (N 1 , N 2 , NDC) with respect to one or more of said plurality of statistical models (θ k ) that identify states of the machining process ( 500 ), said recognition operation ( 300 ) including identification ( 330 ) of one or more causes of defect (D) as a function of the states recognized in said recognition operation.