Primary creep damage may occur at a crack tip in steel at room temperature and below. The effect of this time-dependent damage is generally neglected. Recently developed experimental data clearly show that, for some materials, neglecting time-dependent deformation and damage may be quite nonconservative and dangerous in certain practical applications.In this paper, a new theory is developed which incorporates the effects of time-dependent damage into the crack growth and failure process. The predictive ability of the model is verified first by finite element analyses and then by comparison to experimental data. It is clearly shown that, for the material considered here, time-dependent damage effects must be considered or the crack growth process is not adequately accounted for.