Unless detailed inelastic analysis is followed, high temperature codes base creep relaxation during a dwell period within a cycle on the start-of-dwell equivalent stress. The relaxation of the equivalent stress is then taken to be governed by a uniaxial creep law for the material being considered. Elastic follow-up is also included in such calculations. With this approach, only equivalent values of stress and creep strain rate are obtained and the stress multiaxiality is therefore assumed to remain at its initial value as the stress relaxes. The stress drop is limited to a small fraction (typically 20%) of the initial equivalent stress to ensure that this assumption does not lead to significant inaccuracy. This paper reports creep relaxation results for a pipe subjected to a combination of both primary and secondary stresses. The primary stress is generated by an internal pressure and an axial load, which enable different primary biaxial loading conditions to be generated. The secondary stress is through-wall bending in nature, produced by a through-wall temperature gradient, which influences the initial biaxial stress ratio. Several parameters are varied in order to produce relaxation behaviour in the pipe with an associated elastic follow-up. The starting biaxial stress ratio, the creep law power exponent and the amount of secondary stress result in varying degrees of elastic follow-up being present. The biaxial stress ratio is generally found to change as relaxation occurs and a multiaxial ductility approach is used to evaluate the associated effect on creep damage accumulation. This is compared with the creep damage estimated by assuming relaxation is simply controlled by the equivalent stress with no change in multiaxial stress state during relaxation. It is found that significant equivalent stress drops (up to about 40% of the initial value) can be allowed without the simplified equivalent stress approach being inaccurate. The results have been compared with a number of creep damage models to ensure that the conclusions are not sensitive to the detail of the damage model.