Deterministic and stochastic models are used to examine the evolution of anthelmintic resistance among trichostrongylid parasites of domestic ruminants. We find that the relative selection pressures exerted by chemoprophylactic (preventive) control strategies, chemotherapeutic (salvage) control strategies, and regimens involving "under-dosing" are critically dependent on a variety of host and parasite parameters (particularly host immunity and grazing behaviour, parasite fecundity, and the survival of the free-living stages on the pasture). Chemoprophylactic strategies are not necessarily more likely to exert a stronger selection pressure than chemotherapeutic strategies. Similarly, as one reduces dosage levels, there is a range of dose levels where under-dosing promotes resistance and a range of dose levels where under-dosing impedes resistance. The most dangerous dose is either that necessary to kill all the susceptible homozygotes, or that necessary to kill all the susceptible homozygotes and all the heterozygotes. Which one prevails depends upon model parameters. The stochastic formulation indicates that spatial heterogeneity in transmission may be a significant force in promoting the spread of resistant genotypes--at least when infection is at low levels.