A machine for making steel wire springs has a tray on which are mounted forming tools slidable towards the center of the tray, means for moving the wire perpendicular to the tray, and means for clamping and cutting the wire. The means for moving the wire comprises two alternately operable clamps, one fixed and the other movable, and further includes a cylindrical member rotating in a fixed member integral with the tray. The movable member has an eccentric opening therein for the passage of the wire coacting with an eccentric opening in the fixed member and means are provided for rotating the movable member in such a way as to clamp in a first phase of operation and then cut the wire even with the opening of the fixed member in a second phase of operation.