Gastrointestinal parasitism presents a major constraint on livestock production, resulting in reduced animal performance and welfare. Resistance to gastrointestinal parasitism in sheep, as measured by faecal egg count, is heritable suggesting that selection for increased resistance may be used as a longterm control measure, in addition to existing management strategies. Predicting likely responses to selection for resistance gastrointestinal parasites is a challenging problem, however, because (i) interactions between animals affect the expression of disease resistance traits, and this contravenes the assumptions normally made when predicting responses to selection and (ii) disease severity within a population is rarely shows a Normal distribution, and in the case of gastrointestinal parasitism typically shows a negative binomial distribution. This paper outlines a model which may be used to describe likely responses to selection for resistance to gastrointestinal parasitism in sheep, and presents results obtained from this model.