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As proven, both friction in the gearing and movement of the contact point of the teeth in mesh along the pressure line generate vibrations of the axial components of the resultant force acting in a couple of mating straight bevel gears. The vibrations of the real forces in gearings cause an increased dynamic pressure on and, accordingly, damage of frictional surfaces of differential parts. The law of summing up the axial components of all the gearings in two and four pinion differentials depends on combinations of numbers of the side gear's and pinion's teeth. A classification of bevel gear differentials into four groups depending on those combinations has been carried out. Differentials of the four groups have different degrees of the axial force vibration. The paper presents a detailed method to evaluate theoretically the axial forces in each of the groups. As shown, differentials from one of the four groups (Group III) have decreased axial force vibrations.