  We study the pair production of $B_c$ mesons in the photon-photon interaction
in the framework of perturbative quantum chromodynamics and the relativistic
quark model. The production amplitudes of a pair of pseudoscalar and vector
$B_c$ mesons are constructed in the nonrelativistic approximation and taking
into account relativistic effects. Relativistic corrections related to the
relative motion of heavy quarks in the production amplitude, as well as in the
wave function of the bound state of heavy quarks, are taken into account.
Analytical expressions are constructed for the relativistic differential and
total cross sections for the pair $B_c$ meson production. Based on them,
numerical values of the production cross sections are obtained for various
energies and scattering angles.
