This thesis proposes to use a new model class, the class of Extended State-Affine Systems for identification. It is shown that this model class is able to approximate many nonlinear systems while maintaining limited complexity compared to state-affine systems. Direct identification methods as well as indirect identification methods are proposed for solving the identification problem. Direct methods such as subspace identification methods are used to estimate the system matrices, where structural conditions on the system matrices are derived to where the purely deterministic identification problem can be solved exactly. Based on this exact solution, approximative identification methods are developed in order to be able to approximately solve the identification problem while requiring matrices of lower dimension compared to other methods. In the case of noisy measurements the identification problem is treated using an instrumental variable approach, where it can be shown that under certain conditions asymptotically unbiased estimates can be obtained. If these conditions are not fulfilled nonlinear optimization or indirect methods based on a Structured Total Least Squares approach are proposed for solving the identification problem. Since indirect methods require an additional realization step to obtain the state-space representation, realization methods for extended state-affine systems are discussed.