The dynamics of expansive homeomorphisms with the shadowing property may be very complicated but it is quite well understood (see Aoki and Hiraide's monograph, for example). It is known that these systems admit only a finite number of chain recurrent classes (Spectral Decomposition Theorem - SDT). We will introduce two generalizations of expansivity: N-expansivity and Strong Measure Expansivity. For each natural number N, there is a N-expansive homeomorphism with the shadowing property, where the non-wandering set is total, but it does not satisfy the SDT. On the other hand, systems with the Strong Measure Expansive property satisfy the SDT.