The problem of adaptive compensation of unknown external disturbances is solved for a class of nonlinear systems which have the globally defined normal form. When an a priori unknown external disturbance can be accurately modeled as the output of a linear exosystem of the known order but with unknown parameters, the proposed adaptive controller provides global asymptotic tracking. If the disturbance contains unmodeled components, the proposed controller provides boundedness of all the closed-loop signals and arbitrarily small tracking error.