Some models are presented for the dynamics of a host population with two parasite species. The models differ in two main aspects: whether they include direct competition among parasites and whether the analysis is based on some approximation and which one. If the analysis is not constrained by a priori assumptions about parasite distributions, it is found that species coexistence is very unlikely without some kind of direct competition among parasites; on the other hand, coexistence generally occurs when inter-specific competition is lower than intraspecific, similarly to standard theory for free-living species. If hosts differ in their predisposition to infection, but not in an identical way towards the two parasite species, then species coexistence becomes feasible even if inter-specific competition is as strong as intraspecific; in this case, coexistence becomes easier as the variance in predisposition increases. These models do not yield universal predictions for patterns of parasite distributions; an analysis of the mechanisms of interaction in each specific system is necessary for that.