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Almost perfect nonlinear functions (APN) are of central interest in many mathematical areas such as coding theory and cryptography. In particular, having optimal differential properties, they provide good resistance against differential attack in cryptography. Therefore, many constructions of “infinite classes” of APN functions were introduced in the last years. For example, among those are the functions of Carlet (2011), Zhou–Pott (2013) and Taniguchi (2019), all of which are APN under certain conditions. Another important concept, which plays an essential role against linear attack in cryptography, is the nonlinearity of a function. Therefore, Tan–Qu–Ling–Tan (2013) determined the nonlinearity of the functions given by Carlet, and Zhou–Pott. In this talk, I describe a new method based on Bezout’s theorem to determine the nonlinearity of some classes of quadratic functions, which contain all the classes of APN functions mentioned above. In particular, this approach helps to understand why the majority of the functions in those classes have solely bent and semibent components, which in the case of APN functions is called the classical spectrum. This is a joint work with Tekgül Kalaycı and Wilfried Meidl.