A forging press for rotationally asymmetrical parts by warm or hot forming has a stationary press table, a vertically shiftable press ram above the press table, vertically delimiting with the press table a working space, and vertically displaceable between from an upper open position into a lower closed position. An upper part is carried by the ram in the space, and an upper die in the space is in turn carried on the upper part. A lower part sits on the table in the space and below the upper part and carries a lower die in the space and fittable with the upper die in the closed position. A first closing apparatus outside the space bears vertically on one of the dies, and a second closing apparatus outside the space bears vertically via the first closing apparatus on the one die.