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We analyze the hierarchies of levels in multiscale systems and related description parameters and models. Then as the illustrations we propose some new formulations of problems and solution interpretations. At first we discuss the different types of chaos and turbulence in the hierarchy of levels. Secondly we consider cellular automata models with internal structures of the cells and multivalued solutions. And thirdly we consider the society as multiscale system and its multiscale models. In such investigations we take into account as the memory as the anticipatory effects. For some of the examples above we describe the examples of numerical modeling of system behavior including some types of chaotic behavior and turbulence; micro & macro analogies etc. Further prospects and problems for investigations are described.