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The main objective of this work is to study the asymptotic behavior of the solutions of both functional differential equations and difference equations, through direct methods. For the case of functional differential equations, we use Lyapunoff vector functions, in connection with Razumikhi's idea in order construct appropriate comparison systems. For the case of difference equations, we use the invariants of Minkowski's metric in order to develop a principle which gives useful criteria to determine various kinds of stability, including those of Lagrange and Lyapunoff. Besides this, the above technique is also used in the construction of comparison systems for these equations.