  This second part is devoted to the investigation of global properties of
Prescribed Mean Curvature (PMC) foliations in cosmological spacetimes with
local $U(1) \times U(1)$ symmetry and matter described by the Vlasov equation.
It turns out, that these spacetimes admit a global foliation by PMC surfaces,
as well, but the techniques to achieve this goal are more complex than in the
cases considered in part I.
