  The totally nonnegative part of a partial flag variety G/P is known to have a
decomposition into semi-algebraic cells. We show that the closure of a cell is
again a union of cells and give a combinatorial description of the closure
relations. The totally nonnegative cells are defined by intersecting the
totally nonnegative part with a certain stratification of G/P defined by
Lusztig. We also verify the same closure relations for these strata.
