  The main aim of this paper is to construct explicitly orthogonal bases for
the spaces of k-homogeneous polynomial solutions of the Hodge-de Rham system in
the Euclidean space R^m which take values in the space of s-vectors. Actually,
we describe even the so-called Gelfand-Tsetlin bases for such spaces in terms
of Gegenbauer polynomials. As an application, we obtain an algorithm how to
compute an orthogonal basis of the space of homogeneous solutions of a
generalized Moisil-Theodoresco system in R^m.
