Barenblatt's idea of modeling the crack process zone by means of a cohesive zone has attracted considerable attention for predicting ductile crack growth. The model allows separation of the energy necessary for material separation from global plastic work. This has been a key problem in ductile fracture when searching for reasons for the geometry dependence of crack growth resistance curves. When using cohesive zone models, the correct determination of the cohesive zone material parameters is of eminent importance. In the past these parameters—the cohesive strength and the separation energy—were assumed to be material constants. However, micromechanical considerations show that this assumption is only an approximation in the case of ductile fracture. Here, the underlying mechanisms of void nucleation, growth, and coalescence are dependent on the stress triaxiality. This effect is accounted for in the new constitutive equation for cohesive zone models as presented here. In this new “triaxiality-dependent cohesive zone model,” the cohesive material properties are taken to be dependent on the stress triaxiality in the solid element adjacent to the cohesive element. For low triaxiality, low values of cohesive strength and large values of the separation energy are observed; the opposite holds true for cases of high triaxiality. Ductile crack growth in a mild steel under quasistatic loading was investigated. The results from the use of the triaxiality-dependent cohesive zone model are compared to those of the Gurson-Tvergaard-Needleman (GTN) model as well as to the cohesive zone model with constant material parameters. The dissipation rate is shown to be a favorable measure for the characterization of the crack growth resistance. It allows the description of both the (global) plastic dissipation and the (local) work of fracture.