We present numerical and analytical results on static spherically symmetric solutions of an SU(2) Yang-Mills field coupled to the gravitational field and to a dilaton. For any value of the dilaton coupling constant we find a discrete family of globally regular solutions of finite mass. In addition our analysis indicates the existence of a similar discrete family of black hole solutions for any given radius r h of their horizon. All these solutions turn out to be unstable in linearized perturbation theory.