This paper reviews some results from the theory of fast-slow dynamical systems and presents the detailed analysis of some systems of interest in neuroscience, electrical engineering and fusion plasma physics. The singular perturbation methods are used order to explain the di erent types of oscillations occurring in systems that are obtained by weak perturbations of integrable systems. There are also analyzed systems for which these methods cannot be used and speci c explanations for their oscillatory behavior are found. The results are interpreted from practical point of view.