  Methods developed for the analysis of integrable systems are used to study
the problem of hyperK\"ahler metrics building as formulated in D=2 N=4
supersymmetric harmonic superspace. We show, in particular, that the constraint
equation $\beta\partial^{++2}\omega -\xi^{++2}\exp 2\beta\omega =0$ and its
Toda like generalizations are integrable. Explicit solutions together with the
conserved currents generating the symmetry responsible of the integrability of
these equations are given. Other features are also discussed
