  In this second paper, I construct a limit space of a Cauchy sequence of
globally hyperbolic spacetimes. In the second section, I work gradually towards
a construction of the limit space. I prove the limit space is unique up to
isometry. I als show that, in general, the limit space has quite complicated
causal behaviour. This work prepares the final paper in which I shall study in
more detail properties of the limit space and the moduli space of (compact)
globally hyperbolic spacetimes (cobordisms). As a fait divers, I give in this
paper a suitable definition of dimension of a Lorentz space in agreement with
the one given by Gromov in the Riemannian case.
