  We construct a special class of Lorentz surfaces in the pseudo-Euclidean
4-space with neutral metric which are one-parameter systems of meridians of
rotational hypersurfaces with lightlike axis and call them meridian surfaces.
We give the complete classification of the meridian surfaces with constant
Gauss curvature and prove that there are no meridian surfaces with parallel
mean curvature vector field other than CMC surfaces lying in a hyperplane. We
also classify the meridian surfaces with parallel normalized mean curvature
vector field. We show that in the family of the meridian surfaces there exist
Lorentz surfaces which have parallel normalized mean curvature vector field but
not parallel mean curvature vector.
