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A classification is given for the composite knots and the Dehn surgery on these knots which yield Seifert fibered surgery manifolds. We prove that if a knot K is the composition of two torus knots, then some (unique) integral surgery on K yields a Seifert fibered manifold, and conversely if the surgery manifold of a composite knot K is Seifert fibered, then K is the composition of two torus knots and the surgery must be integral surgery, which is uniquely determined.doi:10.1090/s0002-9939-1990-1002161-6 fatcat:eystsp6xkfavpdp236acj5bw4q