Abstract. We give some characterizations of n dimensional (n ≥ 2) hyperbolic cylinder, spherical cylinder or Euclidean cylinder in a Lorentzian space form. We show that the hyperbolic cylinder, spherical cylinder or Euclidean cylinder is the only complete spacelike hypersurface in an (n+1) dimensional Lorentzian space form M n+1 1 (c) with non-zero constant mean curvature and two distinct principal curvatures one of which is simple, if the norm square of the second fundamental form of M n satisfies some pinching conditions, respectively