Device for applying hooks or clips to the slats of Venetian blinds with folded edges provided with abutment gaskets, comprising: - a guide defining a track along which a slat is positioned, said guide positioning the slat so that the latter is placed in one of the two half-spaces defined by a reference plane (m) with its longitudinal edges (B1, B2) positioned on such reference plane (m); and - at least a first matrix which defines a seat destined to receive a portion of a longitudinal edge of the slat and comprising at least one access aperture to the seat through which hooks or clips are made to enter said seat to be applied to the portion of edge housed therein, said seat being made at the interface between a first portion and second portion into which the first matrix is subdivided, the two portions (11, 12) of the matrix being movable in relation to the reference plane (m) between a closed position, wherein the two portions (11,12) are positioned alongside each other to close the seat around the portion of edge so as to keep the latter blocked in position and permit the application of at least one hook or clip, and at least one open position, wherein the two portions (11,12) of the matrix are distanced from one another to open the seat and thus free the movement of the slat, characterised in that the first portion of the matrix is provided with a projecting appendage destined to skim the edge of the slat, in passing from the open position to the closed position said first portion being movable so as to shift said projecting appendage from a position outside the track to a position inside the track, so that said appendage crosses the edge of the slat staying in the half-space not occupied by the slat and tangent to the reference plane (m), if said slat is provided with an abutment gasket with a covering tongue of the edge said appendage engaging with its movement from the outside position to the inside position said tongue thereby distancing the tongue from the edge and preventing it from being closed inside the seat. - a guide defining a track along which a slat is positioned, said guide positioning the slat so that the latter is placed in one of the two half-spaces defined by a reference plane (m) with its longitudinal edges (B1, B2) positioned on such reference plane (m); and - at least a first matrix which defines a seat destined to receive a portion of a longitudinal edge of the slat and comprising at least one access aperture to the seat through which hooks or clips are made to enter said seat to be applied to the portion of edge housed therein, said seat being made at the interface between a first portion and second portion into which the first matrix is subdivided, the two portions (11, 12) of the matrix being movable in relation to the reference plane (m) between a closed position, wherein the two portions (11,12) are positioned alongside each other to close the seat around the portion of edge so as to keep the latter blocked in position and permit the application of at least one hook or clip, and at least one open position, wherein the two portions (11,12) of the matrix are distanced from one another to open the seat and thus free the movement of the slat, characterised in that the first portion of the matrix is provided with a projecting appendage destined to skim the edge of the slat, in passing from the open position to the closed position said first portion being movable so as to shift said projecting appendage from a position outside the track to a position inside the track, so that said appendage crosses the edge of the slat staying in the half-space not occupied by the slat and tangent to the reference plane (m), if said slat is provided with an abutment gasket with a covering tongue of the edge said appendage engaging with its movement from the outside position to the inside position said tongue thereby distancing the tongue from the edge and preventing it from being closed inside the seat.