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Abstract. It is shown that for two classes of integrals the results of Gaussian quadrature can be extended straightforwardly to the bivariate case. For these classes Gaussian formulae of an arbitrary degree are derived.

Summary. In this paper an approach is outlined to the two-dimensional analogon of the Gaussian quadrature problem. The main results are necessary and sufficient conditions for the existence of cubature formulae which are exact for all polynomials of degree