Creep constitutive equations are derived here to describe creep behaviour of metals at non-proportional loading by generalisation of nonlinear viscoelaticity equations equipped with temporal analogy of time-stress type. To obtain the new equations, integral dependences for the case of degenerative integral operators are first transformed into differential ones. It is shown that the latters imply the kinematic hardening law. In the proposed constitutive equations, mixed hardening is adopted as a composition of three hardening mechanisms connected with translation, size and shape of the potential surfaces respectively. Weight factors of these mechanisms are defined by two material constants which are obtained from the creep data of non-proportional loading. Two measures of isotropic hardening are introduced: the first is the equivalent strain and the second is a non-decreasing parameter. The constitutive equations introduced are evaluated on the base of experimental data on creep behaviour of D16T aluminium alloy and VT3-1 titanium alloy under non-proportional step loading. Comparison of the theoretical results with the experimental data indicates that the former give good predictions of the material responses. Noticeable differences between the two isotropic measures on predicting the isotropic hardening effect appear when the preceding stress vector rotation is not less than 90 โข . The non-decreasing parameters are better in rotations of the kind. ยฉ Elsevier, Paris creep / hardening / stress-rotation / model / anisotropy