Some layer structures of multi-level systems are studied. The concepts of the n-level similarity of systems, the n-level similarity of linked time systems, and ihe hereditary parts of linked time systems are introduced. Some equivalent conditions for then-level similarity of systems and for then-level similarity of linked time systems are also given. Some unsolved questions are posed. A philosophic (or epislemological) axiom is put forward: the existence of any real matter is known by the existences of all particles of some level of the matter, and some relations between the particles. In the final section, several elementary applications of the results are given.