A cyclic creep damage model, previously proposed by the authors, is modified for a better description of the transient creep of D16T alloy observed in the finite strain range under rapidly changing stresses. The new model encompasses the concept of kinematic hardening, which allows us to account for the creep-induced anisotropy. The model kinematics is based on the nested multiplicative split of the deformation gradient, proposed by Lion. The damage evolution is accounted for by the classical Kachanov-Rabotnov approach. The material parameters are identified using experimental data on cyclic torsion of thick-walled samples with different holding times between load reversals. For the validation of the proposed material model, an additional experiment is analyzed. Although this additional test is not involved in the identification procedure, the proposed cyclic creep damage model describes it accurately.