1. Koala Phascolarctos cinereus populations sometimes exhibit eruptive dynamics, increasing to peak abundance and then crashing to low abundance. This dynamic is considered unacceptable because koalas die from starvation and food trees are killed by defoliation. There is concern that such dynamics may be occurring at a number of sites in south-eastern Australia. The only management option is fertility control of females. 2. We constructed a simulation model of koalas interacting with their food supply (manna gum Eucalyptus viminalis) in Mount Eccles National Park, Victoria, Australia. The amount of manna gum leaves consumed changed the survival and fecundity rates of koalas, and the amount of leaves removed changed the survival and transition rates of manna gums. 3. Without fertility control the koala population was predicted to increase to peak abundance within 10-18 years before crashing. The predicted dynamics of manna gum were more variable but abundance increased in most simulations for up to c. 5 years before declining to c. 25% of peak abundance within 20â¿¿30 years and then increasing subsequently. The maximum rate of koala population decline was an important determinant of the interaction between koalas and manna gum. 4. The best management strategy that was analysed involved estimating the number of unsterilized females in the population annually and then sterilizing a variable number to maintain a population of 1000 koalas: this strategy generated the least decline in manna gum at a consistently low cost. However, there was a delay between imposing fertility control and consequent reduction in koala abundance because of high adult female survival rates. Hence manna gum was predicted to decline for 5-10 years before increasing. 5. Synthesis and applications. Our results highlight important time-lags between implementing fertility control, reducing the abundance of a herbivore with high survival rates and subsequent changes in the abundance of its food supply. Our model is useful for understanding how controlling 'overabundant' herbivores impacts upon the dynamics of both the herbivore and its food supply.