To date, all the adaptive control algorithms have been proposed only for strictly proper systems. In this paper, a scheme is proposed to design an adaptive controller for proper systems, To study the robustness of the adaptive controller, both additive and multiplicative types of unmodeled dynamics are considered and can also be allowed to be proper, or even improper. Global bounded input bounded output stability is established, The achievement of a small in the mean tracking error and perfect tracking/rejection of deterministic trajectories/disturbances in the absence of system unmodeled dynamics are discussed. The results are also verified by simulation studies.