  A zero mean curvature surface in the Lorentz-Minkowski 3-space is said to be
of Riemann-type if it is foliated by circles and at most countably many
straight lines in parallel planes. We classify all zero mean curvature surfaces
of Riemann-type according to their causal characters, and as a corollary, we
prove that if a zero mean curvature surface of Riemann-type has exactly two
causal characters, then the lightlike part of the surface is a part of a
straight line.
