<p>It is shown that the horizontal holonomy group of a K-contact sub-Riemannian manifold either coincides with the holonomy group of a Riemannian manifold, or it is a codimension-one normal subgroup of the later group. This implies the classification of the holonomy algebras of K-contact sub-Riemannian manifolds. The question of existence of parallel horizontal spinors, examples, and consequences are discussed.</p>