In this thesis, w e deal with smooth two-dimensional singular perturbation problems . Attention goes to the entry-exit relation for a generic Hopf - or jump breaking mechanism. We introduce the notions of balanced canard solution , slow relation and fast relation function . We show the role of these functions in the creation of relaxation oscillations and related bifurcations patterns , not only in the presence of a generic breaking parameter but also in the absence of such parameter. We also study canard cycles depending on two phase variables and that are broken by two breaking mechanisms . We could also call them two-layer canard cycles . The canard cycles under consideration contain both a turning point and a fast orbit connecting two jump points . At both the turning point and the connecting fast orbit we suppose the presence of a parameter permitting generic breaking . Such canard cycles depend on two parameters ,that we call phase parameters .We study the relaxation oscillations near the canard cycles by means of a map from the plane of phase parameters to the plane of breaking parameters. This paper is organized as follows.In Sect . 2 we recall the definitions and basic theorems and the precise definition of “Hopf breaking mechanism” and “jump breaking mechanism” , together with the essential properties of the transition maps (the local structure theorems) near these breaking mechanisms . In Sect . 3 we study the behaviour near an arbitrary “balanced canard solution” as occurs in “tunnel behaviour” . We also introduced the “slow relation function” and “fast relation function” and their link to the slow divergence integral . Finally , in Sect . 4 , we show how to use these functions in practice in order to prove the occurrence of certain bifurcation patterns of relaxation oscillations . A new proof is forwarded that , although strongly iired by the former one , is shorter and more traarent . At the same time we can make a number of observations pinpointing clearly the difference in bifurcation pattern between a problem without breaking and one with regular breaking . we are presented some new results concerning two-layer canard cycles . We deal with generic situations with the generic balanced canard cycle as most degenerate (and most interesting) case , we also treat the non-generic balanced canard cycle of finite codimension , but restricted to perturbations in which at least one slow connection remains unbroken .