Disturbance attenuation for a class of nonlinear systems under unknown disturbances is addressed in this paper. Based on the Disturbance-Observer-Based Control (DOBC) concept, two design schemes are proposed for external disturbances generated by exogenous systems where the disturbances could be unbounded. One design scheme is obtained by augmenting the estimation of the disturbance into a state estimation and the other is to design a disturbance observer separately and then integrate with a controller. It is shown that under both schemes, disturbances can be effectively rejected and global stability is guaranteed under certain conditions.