Abstract: A torch head is provided for an oxygen-cutting torch machine comprising, in combination, a torch head; a first torch mounted on the torch head for cutting perpendicular cuts; and a second torch mounted on the torch head for cutting at an angle to the perpendicular; the mounting for the second torch having two parallel side shaft members and two parallel cross shaft members, each pivotably attached to the other at spaced locations so as to define a parallelogram swinging means in which the four members move pivotably and in parallel together; the second torch being pivotably mounted to one of the side members so that the second torch can be positioned at an angle to the perpendicular according to the relative movement of the parallelogram members; a reciprocably movable drive means mounted on the torch head for swinging the parallelogram swinging means; a shaft member rotatable about a point fixed to the torch head and having two spaced pivot mountings, one on each side of the fixed point, one pivot mounting b