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We compute the canonical class of certain Rees algebras. Our formula generalizes that of Herzog and Vasconcelos. Its proof relies on the fact that the formation of the canonical module commutes with subintersections in important cases. As an application we treat the classical determinantal ideals and the corresponding algebras of minors.A considerable part of Wolmer Vasconcelos' work has been devoted to Rees algebras, in particular to their divisorial structure and the computation of the canonical module (see [16][17][18]23,28]). In this paper we give a generalization of the formula of Herzog and Vasconcelos [18] who have computed the canonical module under more special assumptions. We show that

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