  Manifest N=2 supersymmetric Toda systems are constructed from the $sl(n,n+1)$
superalgebras by taking into account their complex structure. In the $n\to
\infty$ continuum limit an N=2 extension of the $(2+1)$-dimensional heavenly
equation is obtained. The integrability is guaranteed by the existence of a
supersymmetric Lax pair. We further analyze the properties of the
$(1+1)$-dimensionally reduced system. Its bosonic sector is of hydrodynamical
type. This is not the case for the whole supersymmetric system which, however,
is super-hydrodynamical when properly expressed in terms of a supergeometry
involving superfields and fermionic derivatives.
