We consider the same class of linearly parameterized single-output nonlinear systems identified in [1] in terms of differential geometric conditions. When persistency of excitation conditions are satisfied, the adaptive observers presented in this note guarantee arbitrarily fast exponential convergence both of parameter and state estimates to actual parameters and states, while the adaptive observers in [1] and [2] guarantee only exponential (not arbitrarily fast) convergence. This extends earlier results obtained in [3] for linear systems.