Almost all of the available multiaxial high cycle fatigue (HCF) criteria are proposed based on definition of an equivalent stress expression that is a modified version of a static equivalent stress definition or a static yield function. All the equivalent stress expressions proposed so far in the fatigue analysis field have been expressed in semistationary forms wherein the global cyclic rather than the instantaneous changes are considered. In the present paper, a new technique for instantaneous fatigue equivalent stress definition is introduced based on new concepts of instantaneous (virtual) stress amplitude and instantaneous (virtual) mean stress. Then, new HCF criteria are proposed using two approaches: (1) polynomial approach and (2) integral approach, to overcome the shortcomings of the available criteria. A relevant fatigue life assessment algorithm is also proposed, and results of the available criteria are compared with results of the proposed criteria as well as the experimental results prepared by the author. To introduce a comprehensive study, the criteria are evaluated for components with complicated geometries under proportional, nonproportional, and random nonproportional loadings. Results reveal that predictions of the proposed approaches are more accurate.