Effective conservation of rare carnivores requires reliable estimates of population density for prioritizing investments and assessing the effectiveness of conservation interventions. We used camera traps and capture–recapture analysis to provide the first reliable abundance and density estimates for the common leopard Panthera pardus and clouded leopard Neofelis nebulosa in Manas National Park, India. In 57 days of camera trapping, with a total of 4,275 camera-trap days, we photo-captured 27 individually identified common leopards (11 males, 13 females and three unidentified), and 16 clouded leopards (four males, five females and seven unidentified). The abundance estimates using the M h jackknife and Pledger model M h were 47.0 and 35.6, respectively, for the common leopard, and 21.0 and 25.0, respectively, for the clouded leopard. Density estimates using maximum likelihood spatially-explicit capture–recapture were 3.4 ± SE 0.82 and 4.73 ± SE 1.43 per 100 km2 for the common and clouded leopards, respectively. Spatially-explicit capture–recapture provided more realistic density estimates compared with those obtained from conventional methods. Our data indicates that camera trapping using a capture–recapture framework is an effective tool for assessing population sizes of cryptic and elusive carnivores such as the common and clouded leopards. The study has established a baseline for the long-term monitoring programme for large carnivores in Manas National Park.