A multiaxial, physically based, continuum damage mechanics methodology for creep of welded 9Cr steels is presented, incorporating a multiple precipitate-type state variable, which simulates the effects of strain- and temperature-induced coarsening kinematics. Precipitate volume fraction and initial diameter for carbide and carbo-nitride precipitate types are key microstructural variables controlling time to failure in the model. The heat-affected zone material is simulated explicitly utilising measured microstructural data, allowing detailed investigation of failure mechanisms. Failure is shown to be controlled by a combination of microstructural degradation and Kachanov-type damage for the formation and growth of creep cavities. Comparisons with experimental data demonstrate the accuracy of this model for P91 material.