The effect of texture and dislocation structure on irradiation creep of Zircaloy-2 (irradiated at about 340 K) and Zr-2.5 wt% Nb alloys (irradiated at about 558 K) is studied by means of a self-consistent model. The model relates the creep behaviour of polycrystals to that of single crystals by taking into account the crystallographic texture, dislocation density, grain shape and the intergranular stresses generated due to the crystallographic anisotropy. Three independent creep compliances of the polycrystal obtained from creep tests on a reference material are used to derive the single crystal creep compliances. These are used to calculate the polycrystalline compliances for the remaining materials. At low irradiation temperatures the predicted polycrystalline compliances agree well with the measured values. The observed behaviour can be described by a climb-assisted glide mechanism in which the creep strain is accommodated mainly by prismatic slip with smaller contributions from basal and pyramidal slip systems. At higher irradiation temperatures, the self-consistent approach can also describe well the creep behaviour of Zr-2.5 wt% Nb samples.