The goal of this paper is to examine the robustness of an indirect continuous-time adaptive controller. Parameter projection, which is the only modification on the basis of earlier conventional adaptive control algorithms, is employed to constrain the estimates inside a prior known region. Following the somewhat standard analysis of indirect adaptive control systems, it is shown that, without any restriction on signals in the closed-loop system, such as persistence of excitation, global stability of the system is guaranteed in the presence of unmodelled dynamics and bounded external disturbances. Furthermore, the adaptive controller can still retain the properties of earlier unmodified conventional adaptive controllers when the controlled plant satisfies so-called ’ideal assumptions’. For implementation, no a priori knowledge on the unmodelled dynamics is needed.