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The problem of detecting and recognizing the sounds of fin whales, Balaenoptera physalus, and North Atlantic right whales, Eubalaena glacialis, in the presence ambient noise is considered. A proposed solution is based on a multiple-stage hypothesis-testing technique. The closed form representations of the algorithms are derived, and realizable detection schemes are developed. Empirical tests were conducted using data recordings collected in 2007 off the coast of Massachusetts. Results reveal that the proposed technique is able to detect approximately 80% of the calls detected by the human operator and to produce an average of 12.0 - 33.5 false alarms per 24 h of observation.