  Using photon-photon collisions as a particularly transparent study case we
investigate the production mechanisms for $B_c$ mesons. In nonrelativistic
approximation and to $O(\alpha^2\alpha_s^2)$ it is shown that recombination of
$\bar{b}$- and $c$-quarks dominates by far over $\bar{b}$ and $c$
fragmentation. This dominance persists up to the highest accessible transverse
momenta and leads to distributions in energy which differ completely from the
spectra expected on the basis of the fragmentation functions. For processes in
which a $b \bar{b}$-pair is radiated from a primary $c$-quark, the
fragmentation description is found to be inadequate. We anticipate important
implications of these results for hadronic production of heavy quark
resonances. Using realistic photon spectra we predict two-photon production
rates for $B_c$ and $B_c^*$ at present and future $e^+e^-$-machines.
