A simple approximate method for estimating creep damage in pressure components experiencing multiaxial relaxation and follow-up is presented. The theoretical formulation essentially relates the relaxation process that accounts for multiaxiality and follow-up to the uniaxial relaxation model. The effect of follow-up is determined by studying the relaxation response on the Generalized Local Stress Strain (GLOSS) diagram. A procedure for partitioning creep damage into load and deformation-controlled fractions is also discussed. GLOSS analysis is applied to several component configurations that exhibit follow-up potential.