A swivel head assembly for a dual head oxy-fuel torch which incorporates a fixed oxygen delivery head and a 360 degree rotatable fuel delivery head mounted coaxially upon the oxygen delivery head, such that regardless of whether the torch is pushed forward, drawn backward or manipulated to either side, the fuel delivery head can be readily repositioned relative to the oxygen delivery head so as to always lead the delivery of oxygen for preheating, thus accommodating ease of arm movement and avoiding the need for cumbersome body movement and positioning around the target cutting surface.