First, I will present the Yang-Mills fields on an arbitrary fixed curved space-time, valued in any Lie algebra, and then expose briefly the proof of the non-blow-up of the Yang-Mills curvature. Thereafter, I will present recent results obtained with Dietrich Häfner concerning the Yang-Mills fields on the Schwarzschild black hole. Unlike the free scalar wave equation, the Yang-Mills equations on a black hole space-time admit stationary solutions, which we eliminate by considering spherically symmetric initial data with small energy and satisfying a certain Ansatz. We then prove uniform decay estimates in the entire exterior region of the black hole, including the event horizon, for gauge invariant norms on the Yang-Mills curvature generated from such initial data, including the pointwise norm of the so-called middle components. This is done by proving in this setting, a Morawetz type estimate that is stronger than the one assumed in previous work, without decoupling the middle-components, using the Yang-Mills equations directly.