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In this work we propose to relate the k-determinance of f: Rⁿ, 0 → R^p, 0, relatively to R, L, A, C and K, i) the rank of f and the dimensions n and p, ii) the Boardman' Simbols. Chapters II and III are deal with the case i. Some general theorems are proved and deeper results are given for small values of n and p. The case ii was worked out in the chapter IV. Necessary and sufficient conditions for finite Boardman' Simbols are given. Also we relate the degree of finite determinance with the lenght of the Boardman' Simbols.