The work presents a calculative proof of strength for compensated and case hardened spur gears taking into account the different stress conditions in the tooth root and on the tooth flank. The basis of the proof of stregth is the local comparision of the occured stresses and the allowed stresses in the spur gear. The complex stress condition on the tooth flank is illustrated. On the flank occours a three dimensional stress condition with turnig principial stress systems. Furthermore the influences on this stress condition of residual stresses and of the contact of technical surfaces are discussed. Especially the described complex stress condition on the tooth flank asks for a calculation with an adequate criterion of failure. For this purpose a variant of the Schubspannungsintensitätshypothese (SIH) is proposed. The applicability of the proposed model is verified with numerous results of experiments. Some of the calculations are presented here. Altogether there is a good conformity between the test results and the calculated results especially for the ammount of the fatigue limit, the kind of damage (e.g. tooth root breackage, pitting, tooth breackage in the region of the flank) and the position of the beginning of the damage.