[en] The covariant SU(2) spinning string model of Pernici and van Nieuwenhuizen which has (4,4) supersymmetry is chirally truncated to a (4,0) model. The model is extended by the addition of a locally supersymmetric Wess-Zumino term, and heterotic fermions. This system is coupled to composite as well as fundamental Yang-Mills gauge fields. (author)