We prove that a transcendance condition (C) on the Tayor series of a restricted smooth function h implies the o-minimality of the expansion of the real field by h. This condition is shown to be generic, in the sense that the set of all functions that verify (C) is residual with respect to the Whitney topology. As corollaries, we re-obtain o-minimal structures that does not admit analytic cell decomposition, and non compatible o-minimal structures. We even obtain o-minimal structures which are not compatible with restricted analytic functions.