BPS domain walls in models with flat directions

We consider BPS domain walls in four-dimensional script N = 1 supersymmetric models with continuous global symmetry. Since the BPS equation is covariant under a global transformation, the solutions of the BPS walls also have global symmetry. The moduli space of the supersymmetric vacua in such models has non-cornpact flat directions, and complex BPS walls interpolating between two disjoint flat directions can exist. We examine this possibility in two models with global O(2) symmetry and construct the solutions of such BPS walls.