[en] Using methods developed in Field Theory and Statistical Mechanics, especially in the context of the Anderson model as generalised by Wegner, we develop a novel approach to the Statistical Theory of Nuclear Reactions. We consider a finite set of N bound states, coupled to each other an ensemble of Gaussian orthogonal matrices, and coupled to a set of channels via fixed coupling matrix elements. We evaluate the ensemble average and the variance of the elements of the nuclear scattering matrix, using the method of a generating function combined with the replica trick, followed by the Hubbard-Stratonovitch transformation and a modified loop expansion. In the limit N -> infinite, we show quite generally that, aside from a trivial dependence on average S-matrix elements, the variance depends only on the transmission coefficients, and that the correlation width of a pair of S-matrix elements is given by a universal function of the transmission coefficients. A modified loop expansion yields an asymptotic series valid for strong absorption. The terms in this series are partly novel, and partly coincide with results obtained earlier in the framework of a model which did not take account of the GOE eigenvalue fluctuations. This suggests that average cross sections are mainly sensitive to the stiffness of the GOE spectrum. Fluctuation properties are also derived, and the link to Ericson fluctuation theory is established. (orig.)