  In supersymmetric quantum mechanics, the non-Abelian Berry phase is known to
obey certain differential equations. Here we study N=(0,4) systems and show
that the non-Abelian Berry connection over R^{4n} satisfies a generalization of
the self-dual Yang-Mills equations. Upon dimensional reduction, these become
the tt* equations. We further study the Berry connection in N=(4,4) theories
and show that the curvature is covariantly constant.
