An integral series representation is obtained for non-linear viscoelastic response to an arbitrary strain (or stress) history. The series is arranged so that experimental data can be incorporated directly. Each of the terms has a definite intrinsic meaning that is independent of the choice of strain measure. The first term is a single integral with a non-linear integrand determined completely by single-step creep or relaxation tests. The nth term is obtained directly by the difference, if any is observed, between the experimental results for n-step tests and the prediction based on (n−1)-step data. The series has the distinctive property that it terminates at the nth term whenever the strain (or stress) history is an n-step history.

Previously published experimental data on non-linear viscoelastic behaviour are re-interpreted on the basis of this theory; in most cases they agree very closely with the single integral approximation given by the first term alone.

The generalization to three-dimensional form and the implications of isotropy are also given.