This paper describes a general framework which enables responses to selection for resistance to gastro-intestinal parasites in sheep to be stochastically modelled. The model incorporates between-animal variation for pasture intake, the proportion of larvae ingested from the pasture which survive to become adults, the fecundity of the mature worm, along with density-dependent control of this trait and the mortality rate of the worms. The between-animal variation for each component is partitioned into genetic, permanent and temporary environmental components which vary with age. Infection rates are estimated from existing pasture larval contamination and new contamination from infected animals. Using this framework, selection for reduced mean faecal egg count was practised, in silico, for a period of 10 years. Several general patterns emerged. First, a curvilinear response to selection was observed, with responses initially being large then declining over time. Mean faecal egg count declined from approximately 500 to 140 eggs per gin 10 years and worm burdens and pasture larval contamination showed similar patterns of response. The initial responses to selection were approximately 1·7 times that predicted by quantitative genetic theory because the epidemiology of the disease changed as the animals' genetic resistance improved. A method of partitioning selection responses into components due to the altered genotypes of the animals and components due to altered disease epidemiology is outlined. Secondly, the faecal egg count distribution became more aggregated, or skewed, as selection progressed. Thirdly, correlating pasture contamination levels across years (carry-over effects) resulted in even greater apparent responses to selection. Finally, regular anihelmintic treatment reduced mean faecal egg counts but did not alter the patterns of response to selection, indicating that selective breeding should be feasible under a variety of anthelmintic regimes.