The literature on the time-dependent behaviour of single bast fibres such as flax and hemp is extremely poor. The aim of this extensive study is to characterise the long-term behaviour of elementary hemp fibres and to establish suitable constitutive laws. Single hemp fibres are shown to exhibit both instantaneous strain and delayed, time-dependent strain when tensile loaded under constant climate. The creep behaviour appears to be a logarithmic function of time with a high strain rate during the primary creep and a lower and constant one during the secondary creep. A large scattering both in time-dependent properties and behaviour was observed on a batch of 25 single fibres. Three main creep behaviours were observed. Type II is truly linear as a function of the logarithm of time while Type I and Type III are strongly nonlinear and can be described, respectively, by concave and convex functions. A rheological model based on an anisotropic viscoelastic law and on a truncated inverse Gaussian spectrum of viscous mechanisms was shown to successfully describe all the experimentally observed behaviours.