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We present techniques for generalizing a controller for physics-based walking to significantly different tasks, such as climbing a large step up, or pushing a heavy object. Continuation methods solve such problems using a progressive sequence of problems that trace a path from an existing solved problem to the final desired-but-unsolved problem. Each step in the continuation sequence makes progress towards the target problem while further adapting the solution. We describe and evaluate a number of choices in applying continuation methods to adapting walking gaits for tasks involving interaction with the environment. The methods have been successfully applied to automatically adapt a regular cyclic walk to climbing a 65\n            <jats:italic>cm<\/jats:italic>\n            step, stepping over a 55\n            <jats:italic>cm<\/jats:italic>\n            sill, pushing heavy furniture, walking up steep inclines, and walking on ice. 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