The response of oriented polymer fibres to complex loading patterns is investigated. It is shown that the creep and stress relaxation is nonlinear with the applied stress. The ratio of the creep rate and the stress-relaxation rate is given by the local slope of the tensile curve and not by the elastic modulus as predicted by linear viscoelastic theory. A consequence of this observation is that viscoelastic and yield deformations are coupled. By analysing the results of the step-creep and the strain-relaxation-strain experiments performed on poly(p-phenylene terephthalamide) fibres, it is shown that the linear superposition principle does not apply to the tensile deformation of polymer fibres above the yield point. Finally the various components of the tensile deformation that should be covered by a constitutive equation for polymer fibres are discussed.