System identification finds nowadays application in various areas of biological research as a tool of empiric mathematical modeling and model individualization. A fundamental challenge of system identification in biology awaits in the form of response variability. Furthermore, biological systems tend to exhibit high degree of nonlinearity as well as significant time delays. This thesis covers system identification approaches developed for the applications within two particular biomedical fields: neuroscience and endocrinology. The first topic of the thesis is parameter estimation of the classical Elementary Motion Detector (EMD) model in insect vision. There are two important aspects to be taken care of in the identification approach, namely the nonlinear dynamics of the individual EMD and the spatially distributed structure of multiple detectors producing a measurable neural response. Hence, the suggested identification method is comprised of two consecutive stages addressing each of the above aspects. Furthermore, visual stimulus design for high spatial excitation order has been investigated. The second topic is parameter estimation of mathematical model for testosterone regulation in the human male. The main challenges of this application are in the unavailability of input signal measurements and the presence of an unknown pulsatile feedback in the system resulting in a highly nonlinear closed-loop dynamics. Semi-blind identification method has been developed based on a recently proposed pulse-modulated model of pulsatile endocrine regulation. The two system identification problems treated in the thesis bear some resemblance in the sense that both involve measured signals that can be seen as square-integrable functions of time. This property is handled by transforming the signals into the Laguerre domain, i.e. by equivalently representing the functions with their infinite Laguerre series.