  We consider (flat) Cauchy-complete GH spacetimes, i.e., globally hyperbolic
flat lorentzian manifolds admitting some Cauchy hypersurface on which the
ambient lorentzian metric restricts as a complete riemannian metric. We define
a family of such spacetimes - model spacetimes - including four subfamilies:
translation spacetimes, Misner spacetimes, unipotent spacetimes, and
Cauchy-hyperbolic spacetimes (the last family - undoubtfull the most
interesting one - is a generalization of standart spacetimes defined by G.
Mess). We prove that, up to finite coverings and (twisted) products by
euclidean linear spaces, any Cauchy-complete GH spacetime can be isometrically
embedded in a model spacetime, or in a twisted product of a Cauchy-hyperbolic
spacetime by flat euclidean torus. We obtain as a corollary the classification
of maximal GH spacetimes admitting closed Cauchy hypersurfaces. We also
establish the existence of CMC foliations on every model spacetime.
