This paper reports on line contact skew gears, one of which is a spur gear, where the angle of the gears' axis is free. First, the expression for the subpitch line of the skew gears is derived. Second, the expression for the contact condition of the skew gears on the subpitch line is derived. Characteristics of the expressions are similar to those for spur gears and it is possible to solve the expressions directly. Third expressions of the zone of contact and the opposite tooth surface are derived from the contact condition. Finally, worm gears, one of which is an involute spur gear, are investigated and several findings are obtained.