A transmission model was devised for trichostrongylid nematodes of saiga antelopes and domestic sheep in Kazakhstan. The framework extends previous models by including seasonal migration of saigas, contact with separate populations of sheep, and climate-driven stochasticity in herbage biomass and in the development, survival and migration onto herbage of free-living larvae. The model was parameterised for the contrasting life histories of Marshallagia, Haemonchus and Nematodirus, three important parasites of saigas and sheep in the region, and was successful at predicting broad qualitative patterns of infection dynamics in sheep and saigas. Parasite transmission between saigas and sheep was predicted to be most important for Marshallagia (from sheep to saigas in the south in winter, and onward transmission to sheep in the north in summer) and Haemonchus (from sheep in the north in summer via saigas to sheep further south in autumn). Model predictions for winter transmission of Marshallagia infection in saigas were consistent with field data, which showed that saigas culled before they have grazed the winter range carry lower burdens of this parasite than older animals. The model provides a mechanistic explanation for its predictions, which will assist hypothesis formation, and further the epidemiological basis of efforts to control parasite transmission between wildlife and livestock in both directions. A similar modelling approach could prove useful in other situations where detailed mechanistic models of parasite transmission are inappropriate in the face of parameter uncertainty and spatio-temporal variation in climate and host density. This is likely to include the majority of wildlife-parasite systems.