Generalized creep and relaxation functions, appearing as kernels in the Fréchet‐Green‐Rivlin multiple integral developments of the response functionals, are related by a system of linear Volterra equations of the first order. The general form of these relations is given explicitly in the one‐dimensional case. The kernels of the Volterra equations obtained are the same for every order. They have hence the same resolvent kernel, derived simply from the relaxation function of order one. Furthermore, the relaxation function of order one depends only on the creep function of order one, through an equation identical to that obtained in linear viscoelasticity. The resolution of this last equation (by standard methods used in linear viscoelasticity) gives the solution for higher orders by quadratures. In the case without aging, the usual Carson‐Laplace transform method can be used to solve the first equation and perform the quadratures. These results have been obtained by direct calculations which are a little tedious and are not given here. However, an explicit derivation of the system of Volterra equations is given in the Appendix, for the nonaging case. This derivation is made by use of theHntransform, which is based on the multidimensional Carson‐Laplace transform.