This paper presents an adaptive control scheme for nonlinear systems that violates some of the common regularity and structural conditions of current nonlinear adaptive schemes such as involutivity, existence of a well-defined relative degree, and minimum phase property, While the controller is designed using an approximate model with suitable properties, the parameter update law is derived from an observation error based on the exact model described in suitable coordinates. We show that this approach results in a stable, closed-loop system and achieves adaptive tracking with bounds on the tracking error and parameter estimates. We also present a constructive procedure for adaptive state regulation which is based on the quadratic linearization technique via dynamic state feedback. This regulation scheme does not impose any restriction on the location of the unknown parameters and is applicable to any linearly controllable nonlinear system.