Wearing parts system intended for the tool of a tilling machine of the type which comprises a holder part, attachable to the tool and comprising a holder beak, and a wearing and/or replacement part, detachably arranged at this holder beak and comprising a rear hollow, which is designed to grip the holder beak and is fixed thereto by means of a detachable locking mechanism comprising at least one locking device, placed through interacting openings (28A, 28B, 28C) made through the holder part and the wearing and/or replacement part, the holder beak and the hollow of the wearing and/or replacement part having contact zones (9, 22, 23), each comprising at least two mutually interacting contact faces (10, 25, 26), certain of which only interact with one another after a certain predetermined wear, which contact faces are disposed one on the holder part and one on the wearing and/or replacement part and are intended to absorb vertical, horizontal and collateral forces F x, Fy and F z, of which contact zones (9, 22, 23, wherein - at least one pair of first front contact zones (9a, 9b) is disposed on either side of a symmetry plane including the longitudinal line of symmetry Y of the wearing parts system, whilst at least one pair of first rear contact zones (9c, 9d) forms a certain defined angle with and on either side of the said symmetry plane; - at least one pair of second front and second rear contact zones (9i, 9j and 9g, 9h) are disposed laterally offset in pairs and on either side of the line of symmetry Y; - and said contact zones further comprise, on the one hand, at least one third front contact zone and, on the other hand, at least two third rear contact zones (22, 23), two of which are constituted by interacting joints (22, 23) with common rotational axis Z, which joints (22, 23) each comprise a recess and a projection each comprising a respective joint contact face (25, 26), disposed one on each coupling part (2, 3), characterized in that the common rotational axis Z is arranged essentially perpendicular to the direction of fitting of the locking device, in that the said recesses comprise a respective first end face and in that the projections comprise a respective second end face, which end faces (25, 26) are designed so that the distance between the end faces (25, 26) of the collateral joints (22, 23) at their common centre M0 is equal to zero or substantially less than between collar end faces (17, 18) of the wearing and/or replacement part and the holder part and so that the radius R1 for a respective recess is larger than the radius R2 for a corresponding projection, in order to interact so as, on the one hand, to limit the pushing-on of the wearing and/or replacement part over the holder part and, on the other hand, to ensure that the contact between the joint contact faces (25, 26) will be made, primarily, at the common centre M 0 of the said end faces (25, 26), and secondarily, as the wear has progressed, symmetrically about this mid contact point M 0, at an, due to wear progress, increasingly large contact zone (22', 23'). - at least one pair of first front contact zones (9a, 9b) is disposed on either side of a symmetry plane including the longitudinal line of symmetry Y of the wearing parts system, whilst at least one pair of first rear contact zones (9c, 9d) forms a certain defined angle with and on either side of the said symmetry plane; - at least one pair of second front and second rear contact zones (9i, 9j and 9g, 9h) are disposed laterally offset in pairs and on either side of the line of symmetry Y; - and said contact zones further comprise, on the one hand, at least one third front contact zone and, on the other hand, at least two third rear contact zones (22, 23), two of which are constituted by interacting joints (22, 23) with common rotational axis Z, which joints (22, 23) each comprise a recess and a projection each comprising a respective joint contact face (25, 26), disposed one on each coupling part (2, 3),