Summary We propose an approximate maximum likelihood method for estimating animal density and abundance from binary passive acoustic transects, when both the probability of detection and the range of detection are unknown. The transect survey is purposely designed so that successive data points are dependent, and this dependence is exploited to simultaneously estimate density, range of detection, and probability of detection. The data are assumed to follow a homogeneous Poisson process in space, and a second-order Markov approximation to the likelihood is used. Simulations show that this method has small bias under the assumptions used to derive the likelihood, although it performs better when the probability of detection is close to 1. The effects of violations of these assumptions are also investigated, and the approach is found to be sensitive to spatial trends in density and clustering. The method is illustrated using real acoustic data from a survey of sperm and humpback whales.