  We examine how implicit functions on ILB-Fr\'echet spaces can be obtained
without metric or norm estimates which are classically assumed. We obtain
implicit functions defined on a domain $D$ which is not necessarily open, but
which contains the unit open ball of a Banach space. The corresponding inverse
functions theorem is obtained, and we finish with an open question on the
adequate (generalized) notion of differentiation, needed for the corresponding
version of the Fr\"obenius theorem.
