  We study transversely Lorentzian foliations on the closed 3-manifolds. We
classify them under a completeness hypothesis and we deduce the dual
classification of codimension 1 geodesically complete timelike totally geodesic
foliations. Besides we provide an example of a Lorentzian foliation on a
compact 3-manifold which is equicontinuous on a proper dense open subset of the
manifold, and hence not transversely complete.
