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A new framework to design adaptive controllers for nonlinearly parameterized systems is proposed in this technical note. The key step is the construction of a monotone mapping, which explicitly depends on some of the estimator tuning parameters. Convexity-that is related to monotonicity-has been explored by several authors. The property is assumed a priori and is useful for the design only in some region of state space, which is completed switching the controller. In our approach monotonicity can be used in the whole state space and, moreover, is enforced by the designer, effectively becoming a synthesis tool. One consequence of these features is that the controller does not rely on state-dependent switching. In order to dispose of degrees of freedom to render the function monotone we depart from standard adaptive control and adopt instead the recently introduced Immersion and Invariance approach.