  The global and semi-global analytic hypoellipticity on the torus is proved
for two classes of sums of squares operators, introduced in "Analytic
Hypoellipticity for Sums of Squares and the Treves Conjecture" by P. Albano and
A. Bove and M. Mughetti, and in "Analytic Hypoellipticity for Sums of Squares
and the Treves Conjecture. II" by A. Bove and M. Mughetti, satisfying the
H\"ormander condition and which fail to be neither locally nor microlocally
analytic hypoelliptic.
