The aim of the present work is to show that many notions of holomorphic maps in the framework of locally convex spaces (l.c.s.) or bornological vector spaces (b.v.s.) are in fact reducible to only one definition given by J. S. e Silva in [11]. We consider only definitions satisfying the following conditions: 1 ) they generalize the notion of an analytic map in Banach spaces, 2) their theories are valid in the "usual" spaces, 3) the usual bilinear maps are holomorphic, and it seems to us indispensable to demand that these three conditions should be satisfied.