Methods are developed for estimating the size/density of cetacean populations using data from a set of fixed passive acoustic sensors. The methods convert the number of detected acoustic cues into animal density by accounting for (i) the probability of detecting cues, (ii) the rate at which animals produce cues, and (iii) the proportion of false positive detections. Additional information is often required for estimation of these quantities, for example, from an acoustic tag applied to a sample of animals. Methods are illustrated with a case study: estimation of Blainville's beaked whale density over a 6 day period in spring 2005, using an 82 hydrophone wide-baseline array located in the Tongue of the Ocean, Bahamas. To estimate the required quantities, additional data are used from digital acoustic tags, attached to five whales over 21 deep dives, where cues recorded on some of the dives are associated with those received on the fixed hydrophones. Estimated density was 25.3 or 22.5 animals/1000 km(2), depending on assumptions about false positive detections, with 95% confidence intervals 17.3-36.9 and 15.4-32.9. These methods are potentially applicable to a wide variety of marine and terrestrial species that are hard to survey using conventional visual methods.