  We construct a special class of spacelike surfaces in the Minkowski 4-space
which are one-parameter systems of meridians of the rotational hypersurface
with lightlike axis and call these surfaces meridian surfaces of parabolic
type. They are analogous to the meridian surfaces of elliptic or hyperbolic
type. Using the invariants of these surfaces we give the complete
classification of the meridian surfaces of parabolic type with constant Gauss
curvature or constant mean curvature. We also classify the Chen meridian
surfaces of parabolic type and the meridian surfaces of parabolic type with
parallel normal bundle.
