On Aotea/Great Barrier Island, New Zealand, two invasive rat species (Pacific rats and ship rats) pose risks to the ecosystems and challenge the management in two sanctuaries. At Glenfern Sanctuary (83 ha) an eradication has successfully removed ship rats and a predator-proof fence prevents reinvasion. However, Pacific rats persist in low abundance. At Windy Hill Sanctuary (770 ha) intensive rodent control maintains both species at low abundance despite ongoing reinvasion. A capture-mark-recapture study was conducted between February and April in 2016 and repeated between July and September 2017 to determine population densities, confirm species composition, and analyse the effects of time, population density, and interspecific competition on rat behaviour. Live traps were monitored with camera traps to analyse behaviour of rats around traps. Population density and detection probability of Pacific rats varied between times reflecting seasonality in food abundance and rat reproduction. The detection probability of Pacific rats also differed between sites, being higher at Glenfern Sanctuary than at Windy Hill Sanctuary, presumably due to interspecific competition with ship rats. Where Pacific rats were the sole species they were captured in traps in the first night. However, in coexistence with ship rats, Pacific rat detection was delayed by at least ten days. Population density influenced the number of trap encounters and interactions but did not significantly influence the capture rate. Interspecific competition was identified as problematic for monitoring, controlling, and eradicating Pacific rats.