The investigation of the single step stress relaxation behaviour of three polymer fibres, namely Nomex, Kevlar and polypropylene, differing widely in their mechanical properties, shows that a consistent systemization can be applied on the basis of a two-component (TC) model. The model comprises a relaxation function, based on the cumulative log-normal distribution, with a shape that is independent of the type of material and of the strain level. The limits of linearity for viscoelastic behaviour in stress relaxation are deduced and the specific sources of non-linear effects are discussed. For each of the fibres the applicability of simpler models, related to thermorheologically simple or complex materials, is discussed. The results deduced for the stresses and moduli of the elastic and viscous components of the model are plausibly explained on the basis of current models for the fibre structures. The changes of the mean relaxation times with strain are consistent with a solid/fluid transition in an amorphous ’matrix’ component initiated at the yield point for Nomex and polypropylene fibres and with the more ’metal-like’ nature of Kevlar.