  It is demonstrated that there is anti-ferromagnetic spin-spin interaction
between nearest electrons in the 2D Wigner crystal. This is also valid for the
Wigner liquid - the state with destroyed long-range order but preserved
short-range one. We calculate the value of the anti-ferromagnetic interaction
(both analytically and numerically) and discuss a possible magnetic state of
the Wigner crystal. This state can be strongly influenced by the spin-Peierls
mechanism.
