Polymer matrix composites, and especially short glass fibre reinforced polyamides, are widely used in the automotive industry. Their application on structural components requires a confident mechanical design taking into account the sensitivity of the mechanical response to both temperature T and relative humidity H. In this paper, the constitutive model already developed by the authors (Launay et al., 2011) is applied to describe the non-linear time-dependent behaviour of a PA66-GF35 under various hygrothermal conditions. The extensive experimental database involves testing conditions under and above the glass transition temperature Tg. An equivalence principle between temperature and relative humidity is applied and validated, since the non-linear mechanical response is shown to depend only on the temperature gap T-Tg(H).