Hyperparasites in the form of cytoplasmic RNA elements have been proposed as a biological control agent for Dutch elm disease. We characterized the range of outcomes likely to follow the introduction of such an agent by modelling the resultant population dynamics as an ecological interaction between the wild, ‘target’, fungus and the hyperparasitized ‘control’fungus. We used data from the 1970s epidemic of Dutch elm disease in the UK to parameterize the population dynamics of the target fungus, and considered the success of control across a wide range of possibilities for the lethality and transmissibility of the modified control fungus. We decomposed hyperparasite transmissibility into horizontal transmissibility (the ability to colonize previously unparasitized target fungal hosts) and vertical transmissibility (the ability of control fungus to establish new colonies). There is an invasion threshold for both horizontal and vertical transmissibility. As vertical transmission is further increased, there is another threshold at which the target fungus is eradicated because of competitive exclusion by the control fungus. In contrast, eradication by raising horizontal transmission may never succeed because the target fungus needs to be present to support new cases through this route. Between these two thresholds for invasion and exclusion, control and target fungus may coexist. Using a stochastic, spatially extended model, we showed that predictions of success based on high competitive ability of the control fungus (i.e. high vertical transmission) are likely to be more robust than those based on the high degree to which the control fungus can cause target fungus to be hyperparasitized (i.e. high horizontal transmission).