We investigate the Galois module structure of wildly ramified extensions. We are interested in particular in the second invariant of an extension of number fields defined by Chinburg via the canonical class of the extension and lying in the locally free class group. We show that in Queyrut's S-class group, where S is a (finite) set of primes, the image of Chinburg's invariant equals the stable isomorphism class of the ring of integers and thus extend Chinburg's result for tame extensions. 1996Academic Press, Inc.