RESUMEN

We have applied the Painleve criterion to the supersymmetric nonlinear Schrödinger equation. This particular system of fermionic and bosonic field shows up a rich spectrum of resonances and it can be explicitly proved that the expansion coefficients at the resonance positions can remain arbitrary. At this point it is worth noting that even when the extra nonlinear field (which is fermionic in this case) is considered to be bosonic, the resulting system turns out to satisfy the Painleve test so that this second system may be thought of as a new completely integrable system whose Lax pair is still to be found.