The analysis of nonlocal fracture criteria which have recently developed in the framework of the theory of critical distances is carried out. A common property of these criteria is the introduction of the intrinsic length of the material characterizing its microstructure, which allows one to describe the size effect under stress concentrations, thereby expanding the scope of application in comparison with conventional criteria. At the same time, it is marked that this region is limited to cases of brittle or quasi-brittle fracture with a small fracture process zone. To expand the scope of the criteria for cases of fracture with a developed fracture process zone, it is proposed to abandon the hypothesis of the size of this zone as a material constant, associated only with the microstructure of the material. New nonlocal criteria for quasi-brittle fracture are proposed, which are the development of the average stress criterion, and point stress criterion, and which contain a complex parameter that characterizes the size of the fracture process zone and accounts not only for the material microstructure, but also ductile properties of the material, geometry of the specimen, and its loading conditions. The size of the fracture process zone is represented as the sum of two terms, one of which characterizes the material microstructure itself, and the other one refers to the zone of inelastic deformations, whose size is determined by the features of the structural member (notch shape, notch size, loading conditions) and ductile properties of the material. Formulae are obtained for the critical stress in the problem of tension or compression of the plate with a circular hole. The results of calculations are in good agreement with the experimental data.