Numerical calculations for the production of the P-wave levels of B-c
mesons in gamma gamma collisions are performed in the leading order (a
lpha(s)(2) alpha(2)) of perturbation theory. The total cross section f
or the production of P-wave states is about 10% of the cross section f
or the production of S-wave levels. The contribution of the fragmentat
ion component (6+6 diagrams) is small. The main contribution is associ
ated with the recombination mechanism (8 Feynman diagrams). The contri
bution of the fragmentation (b) over bar-->B-c (6 diagrams) is consist
ent with the prediction of the fragmentation model, while the contribu
tion of the fragmentation c-->B-c deviates strongly from the predictio
ns of this model.