The invention relates to a wearing parts system (1) intended for the tool of a tilling machine of the type which comprises a holder part (3), having a front end part (8), and an exchangeable wearing and/or replacement part (2), arranged over this end part and comprising a hood-shaped (6) hollow (7) which, when the wearing part (2) is fitted in place, is designed to grip over the end part and is fixed thereto by means of at least one locking device (27) placed through interacting openings (28), the end part and the hollow having front, rear and collateral contact zones (9, 22, 23), each comprising contact faces (10, 25, 26), disposed one on the holder part and one on the wearing part, for the absorption of acting vertical, horizontal and collateral forces Fx, Fy and Fz. The contact faces (25, 26) are designed to interact so as, on the one hand, to limit the pushing-on of the wearing part over the holder part and, on the other hand, to ensure that the contact between the contact faces will be made, primarily, at the common centre M0, of the two radii (of a recess and a projection) essentially in the horizontal plane YZ and secondarily, as the wear has progressed, symmetrically about this mid contact point as an increasingly large contact zone (22′, 23′).