This paper is devoted to the adaptive control design for a class of nonlinearly parameterized systems assuming the so-called generalized matching condition. A simple adaptive controller with a linear-in-parameter-like structure is designed to account for general parameter-dependent plant nonlinearities. An important feature of our approach is that compactness of parameter sets is not required. Global boundedness of the overall adaptive system and convergence to zero equilibrium state with any prescribed accuracy are established. Our construction technique takes advantage of Lipschitzian properties with respect to the parameter of the plant nonlinearity.