This thesis is about some issues in system modeling: The first is a parsimonious representation of MISO Hammerstein system, which is by projecting the multivariate linear function into a univariate input function space. This leads to the so-called semiparamtric Hammerstein model, which overcomes the commonly known “Curse of dimensionality” for nonparametric estimation on MISO systems. The second issue discussed in this thesis is orthogonal expansion analysis on a univariate Hammerstein model and hypothesis testing for the structure of the nonlinear subsystem. The generalization of this technique can be used to test the validity for parametric assumptions of the nonlinear function in Hammersteim models. It can also be applied to approximate a general nonlinear function by a certain class of parametric function in the Hammerstein models. These techniques can also be extended to other block-oriented systems, e.g, Wiener systems, with slight modification. The third issue in this thesis is applying machine learning and system modeling techniques to transient stability studies in power engineering. The simultaneous variable section and estimation lead to a substantially reduced complexity and yet possesses a stronger prediction power than techniques known in the power engineering literature so far.