  A family of degenerate domain wall configurations, partially preserving
supersymmetry, is discussed in a generalized Wess-Zumino model with two scalar
superfields. We establish some general features inherent to the models with
continuously degenerate domain walls. For instance, for purely real
trajectories additional "integrals of motion" exist. The solution for the
profile of the scalar fields for any wall belonging to the family is found in
quadratures for arbitrary ratio of the coupling constants. For a special value
of this ratio the solution family is obtained explicitly in terms of elementary
functions. We also discuss the threshold amplitudes for multiparticle
production generated by these solutions. New unexpected nullifications of the
threshold amplitudes are found.
