Numerical calculations for the production of P-wave levels of B-c quar
konium in gamma gamma collisions are performed in the leading O(alpha(
s)(2) alpha(em)(2)) order of perturbation theory. The total cross-sect
ion of P-wave state production is about 10% of that for the S-wave lev
els. The contribution of fragmentation component (6 + 6 diagrams) is l
ow, and the basic contribution is determined by the recombination mech
anism (8 Feynman diagrams). The gauge invariant term of the (b) over b
ar --> B-c fragmentation (6 diagrams) quite accurately reproduces the
result of the fragmentation model, whereas there is a strong deviation
of the c --> B-c fragmentation term from the predictions of the fragm
entation model.