The thesis considers methods for the identification of weakly nonlinear systems, met in mixed analog-digital systems for data-transmission. Depending on the available knowledge about the system to be identified different algorithms and model structures can be applied. Thus, one distinguishes between glass-box, gray-box and black-box methods. The contribution of the thesis to the glass-box methods is a scheme for the automatic determination of the Volterra kernels of a weakly nonlinear circuit utilizing Kronecker products. In the field of gray-box methods a model structure and its parameter estimation is presented that allow to incorporate the available knowledge about the linearization of the weakly nonlinear system efficiently into the identification. Black-box methods are extended through the application of model-complexity regulating algorithms from the area of machine learning. Furthermore the relation between the accuracy of the identification and properties of the excitation signal for the identification is investigated and a signal optimization method is proposed. The developed methods are presented using an exemplary circuit and are also applied to the identification of a VDSL (very-high data rate digital subscriber line) line driver circuit.