Intraguild predators both feed on and compete with their intraguild prey. In theory, intraguild predators can therefore be very effective as biological control agents of intraguild prey species, especially in productive environments. We investigated this hypothesis using the mixotrophic chrysophyte Ochromonas as intraguild predator and the harmful cyanobacterium Microcystis aeruginosa as its prey. Ochromonas can grow photoautotrophically, but can also graze efficiently on Microcystis. Hence, it competes with its prey for inorganic resources. We developed a mathematical model and parameterized it for our experimental food web. The model predicts dominance of Microcystis at low nutrient loads, coexistence of both species at intermediate nutrient loads, and dominance of Ochromonas but a strong decrease of Microcystis at high nutrient loads. We tested these theoretical predictions in chemostat experiments supplied with three different nitrogen concentrations. Ochromonas initially suppressed the Microcystis abundance by > 97% compared to the Microcystis monocultures. Thereafter, however, Microcystis gradually recovered to -20% of its monoculture abundance at low nitrogen loads, but to 50-60% at high nitrogen loads. Hence, Ochromonas largely lost control over the Microcystis population at high nitrogen loads. We explored several mechanisms that might explain this deviation from theoretical predictions, and found that intraspecific interference at high Ochromonas densities reduced their grazing rates on Microcystis. These results illustrate the potential of intraguild predation to control pest species, but also show that the effectiveness of their biological control can be reduced in productive environments.