Recently, a new class of adaptive control schemes, motivated from nonlinear systems theory, has been proposed for minimum phase linear time invariant plants. Under certain assumptions on the plant transfer function, these schemes guarantee uniform signal boundedness and good transient and steady-state response for the regulation or tracking error. Despite the good performance properties of the proposed schemes, their practicality relies very much on their robustness properties with respect to plant model uncertainties. These robustness properties have to be established and understood for application purposes. The purpose of this paper is to analyse the stability properties of this new class of adaptive controllers in the presence of ’reasonable’ classes of plant model uncertainties. We first indicate that the same nonrobust behaviour that appears in the case of the traditional adaptive controllers without modifications may be exhibited by this new class of adaptive controller. We then propose design modifications and establish robustness with respect to a general class of multiplicative plant perturbations and bounded input-output disturbances.