  We show that any 3+1-dimensional Milne model is future nonlinearly,
asymptotically stable in the set of solutions to the Einstein-Vlasov system.
For the analysis of the Einstein equations we use the
constant-mean-curvature-spatial-harmonic gauge. For the distribution function
the proof makes use of geometric L^2-estimates based on the Sasaki-metric. The
resulting estimates on the energy momentum tensor are then upgraded by
employing the natural continuity equation for the energy density.
