There are many practical applications in the power and propulsion industries that involve sustained periods of loading at high temperatures with periodic unloading-reloading sequences. Such histories may often be regarded as creep-dominated when only a small number of unloading-reloading events occurs over the life of the component. Typically, thermal constraint additionally results in rotation of the principal stress axes with respect to fixed material axes in regions of stress and temperature gradients, such as nozzle inlets. This rotation may produce anisotropic states of both creep damage and inelastic deformation. Such rotations also occur in the creep zone for an advancing creep crack or if far-field tractions change nonproportionally. In this paper, a continuum creep damage approach is coupled with a rate-dependent bounding surface theory to correlate nonproportional, axial-torsional experiments conducted on thin-walled tubular specimens of Type 304 stainless steel at 593C. A directionally dependent scalar damage distribution evolves as a second-order, symmetric tensor for each unique set of principal stress axes for this material, based on quantitative metallographic assessment of the damage distribution. A general higher order symmetric damage growth law is also introduced.