  Using a $q$-deformed Moyal algebra associated with the group of area
preserving diffeomorphisms of th two-dimensional torus $T^2$, sdiff$_q (T^2)$,
a $q$-deformed version for the Heavenly equations is given. Finally, the
two-dimensional chiral version of Self-dual gravity in this $q$-deformed
context is briefly discussed.
