  We give a conformal representation in terms of meromorphic data for a certain
class of spacelike surfaces in the Lorentz-Minkowski 4-space L^4 whose mean
curvature vector is either lightlike or zero at each point. This representation
extends simultaneously the Weierstrass representation for minimal surfaces in
Euclidean 3-space and for maximal surfaces in the Lorentz-Minkowski 3-space,
and the Bryant representation for mean curvature one surfaces in the hyperbolic
3-space and in the de Sitter 3-space.
