  Using the theory of exterior differential systems, we study the existence of
germ of pseudo-holomorphic disk in a real analytic hypersurface locally defined
in a complex manifold equipped with J a real analytic almost complex structure.
The integrable case in C n with J the multiplication by i has been intensively
studied by several authors [DF], [DA1] and [DA2] for example. The non
integrable case is drastically different essentially due to the following fact
: in generic case, there is no J-invariant objects of dimension bigger than
one. This simple observation leads to the non existence of some equivalents of
Segree varieties or ideals of holomorphic functions which play a fundamental
role in the complex case. Nevertheless in the almost complex case, we adopt the
exterior differential system point of view of E.Cartan developed and clarified
in [BCGGG].
