  Having fixed a Kaehler class and the unique corresponding hyperkaehler
metric, we prove that all special Lagrangian submanifolds of an irreducible
symplectic 4-fold X are bi-Lagrangian and that they are obtained by complex
submanifolds via a sort of "hyperkaehler rotation trick"; thus they retain part
of the rigidity of complex submanifolds: indeed all special Lagrangian
submanifolds of X turn out to be real analytic.
