  We study the evolution of the relation between half-light (effective) radius,
r_e, and mean surface brightness, mi_e, known as Kormendy relation, out to
redshift z=0.64 in V-band restframe on the basis of a large sample of
spheroidal galaxies (N=228) belonging to three clusters of galaxies. The
present sample constitutes the largest data set for which the Kormendy relation
is investigated up to a look-back time of 6 Gyr (H_0= 70 Km/s/Mpc, Omega_M=0.3,
Omega_Lambda=0.7). A new fitting procedure, which suitably accounts for
selection criteria effects, allows for the first time to study the trend of the
slope (beta) and of the intrinsic dispersion (sigma_mi_e) of the Kormendy
relation, and the properties of the whole distribution in the r_e -- mi_e,
plane as a function of look-back time. The slope beta of the relation does not
change from z=0.64 to the present epoch: beta=2.92+/-0.08, implying a tight
constraint of 18--28% on the variation of the stellar formation epoch along the
sequence of spheroidal galaxies per decade of radius. The intrinsic dispersion
of the relation, sigma_i_<mi>_e=0.40+/-0.03, does not vary with redshift and
the distribution of galaxy sizes as well as the distribution in the plane of
the effective parameters do not vary among the clusters, as proven by the
Kolmogorov--Smirnov tests. We conclude that, whatever the mechanism driving
galaxy evolution is, it does not affect significantly the properties of bright
galaxies in the log(r_e) -- mi_e, plane at least since z=0.64. The evolution of
the zeropoint of the Kormendy relation is fully explained by the cosmological
dimming in an expanding universe plus the passive luminosity evolution of
stellar populations with high formation redshift (z_f>2).
