  The extended Yang-Mills gauge theory in Euclidean space is a renormalizable
(by power counting) gauge theory describing a local interacting theory of
scalar, vector, and tensor gauge fields (with maximum spin 2). In this article
we study the quantum aspects and various generalizations of this model in
Euclidean space. In particular the quantization of the pure gauge model in a
common class of covariant gauges is performed. We generalize the pure gauge
sector by including matter fermions in the adjoint representation of the gauge
group and analyze its N=1 and N=2 supersymmetric extensions. We show that the
maximum half-integer spin contained in these fermion fields in dimension 4 is
3/2. Moreover we develop an extension of this theory so as to include internal
gauge symmetries and the coupling to bosonic matter fields. The spontaneous
symmetry breaking of the extended gauge symmetry is also analyzed.
