N = 4 superextension of the dionville equation with quaternion structure

N=4 supersymmetrical extension of the Liouville equation is constructed. It has the interval SU(2)XSU(2) gauge symmet-- ry and can be formulated adequately in terms of the real N=4 quaternion superfield which is subject to certain Grassmanian analyticity conditions. Dynamical equations as well as analyticity conditions are derived from the zero curvature representation on the SU(1, 1|2) superalgebra The system obtained is invariant under transformations of the infinite-dimensional SU(2)-superstring superalgebra while the realization of these transformations is different from those known before A possible connection between the N=4 Liouville theory and the theory of the SU(2)-superstring is discussed