In this paper, we propose a new totally decentralized adaptive output tracking scheme for a class of nonlinear interconnected systems by using a backstepping approach. In the design, a smooth function is introduced to compensate for the effects of interactions from other subsystems. It is shown that the designed local adaptive controllers can ensure all the signals in the closed loop system are bounded. A root mean square type of bound is obtained for the tracking error as a function of design parameters. This implies that the transient tracking error performance can be adjusted by choosing suitable design parameters.