The Brodsky-Lepage (BL) formalism in perturbative QCD is applied to es
timate the validity of the heavy-quark effective theory and the high-e
nergy scaling laws to the exclusive heavy-meson pair production in two
-photon collisions as well as e+e- annihilation. In addition to the or
dinary heavy mesons such as B and D, the heavy mesons of which both qu
ark masses are larger than the typical strong interaction scale LAMBDA
(QCD) are considered. Explicit forms of transition amplitudes are pres
ented for the heavy mesons with two heavy quarks in the peaking approx
imation and the modifications for the ordinary heavy-meson production
are described. The result in the heavy-quark a certain range of center
of mass certain range of center of mass energy. In the high energy li
mit, the transition amplitudes turn out to comply with the high energy
scaling laws. The common features and different points of the e+e- an
d gammagamma cases are described in detail. The limitation of the BL f
ormalism and the heavy-quark effective theory is discussed.