This thesis is devoted to the study of limit cycles appearing in singularly perturbed families of planar vector fields. We consider an ? -family of vector fields on a 2-manifold that, for ? = 0, has a curve of singular points. Such a curve will be called a slow curve and will be denoted S . In general, S consists of hyperbolically attracting points, hyperbolically repelling points and fold points, depending on whether the linear part of the vector field at that point of S has a negative nonzero eigenvalue, a positive nonzero eigenvalue, or 2 zero eigenvalues. we will only consider fold points of nilpotent type. The main subject that we deal with, is to describe the dynamics near a so-called slow–fast system, focusing first on common slow–fast cycles.