Data collected under a double-count protocol during line transect surveys were analyzed using new maximum likelihood methods combined with Akaike's information criterion to provide estimates of the abundance of polar bear (Ursus maritimus Phipps) in a pilot study off the coast of Alaska. Visibility biases were corrected by modeling the detection probabilities using logistic regression functions. Independent variables that influenced the detection probabilities included perpendicular distance of bear groups from the flight line and the number of individuals in the groups. A series of models were considered which vary from (1) the simplest, where the probability of detection was the same for both observers and was not affected by either distance from the flight line or group size, to (2) models where probability of detection is different for the two observers and depends on both distance from the transect and group size. Estimation procedures are developed for the case when additional variables may affect detection probabilities. The methods are illustrated using data from the pilot polar bear survey and some recommendations are given for design of a survey over the larger Chukchi Sea between Russia and the United States.