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Several time-dependent mechanisms are operational in the crack growth process of Ni-base superalloys at elevated temperature. Creep deformation during periods of sustained loading, oxygen diffusion at the crack tip, and oxidation reactions at and in front of the crack tip all contribute to the kinetics of crack growth. A crack growth rate model has been derived that attempts to capture the physics of these various rate processes. The proposed model assumes small-scale creep at the crack tip and incorporates the Hutchison-Rice-Rosengren stress field equations to satisfy this condition. The model also includes stress-assisted diffusion of an environmental species at the crack tip. A process reaction rate is related to the time-rate of crack growth providing a model that accounts for these time-dependent processes. An evaluation of the form of the model is provided by comparison of the model with experimental crack growth data.