  We study the late-time behavior of spherically symmetric solutions of the
Yang-Mills equations on Minkowski and Schwarzschild backgrounds. Using
nonlinear perturbation theory we show in both cases that solutions having
smooth compactly supported initial data posses tails which decay as $t^{-4}$ at
timelike infinity. Moreover, for small initial data on Minkowski background we
derive the third-order formula for the amplitude of the tail and confirm
numerically its accuracy.
