The effects of the meson-exchange currents in the elastic scattering o
f polarized electrons by polarized nuclei are investigated. In particu
lar some stable doubly closed-shell +/- 1 nucleon nuclei are considere
d in the framework of the extreme shell model. We set the conditions o
f observability of such effects and present the situations where such
conditions are fulfilled for the studied nuclei: B-11, C-13, 15, O-17
and K-39. Different target polarizations have been considered. We find
that the most advantageous cases correspond to an on-plane polarized
target and a polarized electron beam, simultaneously.