In this study, crack growth under steady state creep conditions is analysed. A theoretical framework is introduced in which the constitutive behaviour of the bulk material is described by power-law creep. A new class of damage zone models is proposed to model the fracture process ahead of a crack tip, such that the constitutive relation is described by a traction-separation rate law. In particular, simple critical displacement, empirical Kachanov type damage and micromechanical based interface models are used. Using the path independency property of the C ∗ -integral and dimensional analysis, analytical models are developed for pure mode-I steady-state crack growth in a double cantilever beam specimen (DCB) subjected to constant pure bending moment. A computational framework is then implemented using the Finite Element method. The analytical models are calibrated against detailed Finite Element models. The theoretical framework gives the fundamental form of the model and only a single quantity C ^ k needs to be determined from the Finite Element analysis in terms of a dimensionless quantity ϕ 0 , which is the ratio of geometric and material length scales. Further, the validity of the framework is examined by investigating the crack growth response in the limits of small and large ϕ 0 , for which analytical expression can be obtained. We also demonstrate how parameters within the models can be obtained from creep deformation, creep rupture and crack growth experiments.