This paper presents results concerning the identification of a class of nonlinear systems. The main result of the paper gives the approximation power of a parametrized linearization family constructed from a given nonlinear system. The identification procedure derived from this approximation theory consists of constructing a parametrized linearization family from a set of input-output measurements of a given nonlinear system along a given trajectory. This paper utilizes related work on control-oriented system identification. Simulation results are included to support the theoretical development.