In this paper a general approach is taken to yield a characterization of the class of stable plant controller pairs which is a generalization of the Youla parameterization for linear systems. This is based on the idea of representing the input-output pairs of the plant and controller as elements of the kernel of some related operator which is denoted the kernel representation of the system. It is demonstrated that in some sense the kernel representation is a generalization of the left coprime factorization of a general nonlinear system, Results giving one method of deriving a kernel representation for a nonlinear plant with a general state-space description are presented.