1. A method for monitoring the quality of laser-machining processes, wherein the method comprises the operations of: acquiring via sensor means, 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; making available 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, and wherein said method further comprises the operations of: comparing 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 a plurality of statistical models (θ k ) that identify respective states of the machining process, said states including states of defect (D); and executing in real time an operation of recognition 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, said recognition operation including identification of one or more causes of defect (D) as a function of the states recognized in said recognition operation.