It has been theoretically proven that both friction in two mating gears and the drawing of mating involute tooth profiles along the pressure line (the line of action) generate oscillation of axial force components of the resultant force acting in a single pair of mating spur bevel gears. The law of summing the axial force components acting on the side gear from all the differential satellites (pinions), as well as on the pinion from the two side gears, depends on combinations of numbers of teeth on the side gear and pinion. A classification of bevel gear differentials into four groups depending on these combinations has been carried out in the present work. A designer should ensure that a differential under development be in accordance with group III to decrease oscillation of the total axial forces acting inside the mechanism itself. Testing has corroborated the theoretical solutions.