  The production of the B_c and B_c^* mesons was studied in the framework of
the factorization formalism and perturbative QCD. Predicted results implied
that an observable number of B_c and B_c^* events can be produced at LEP I and
at Tevatron. The fragmentation approximation describes the production of the
B_c and B_c^* mesons very well in high energy e^+e^- collisions. In hadronic
collisions, it is valid when and only when the transverse momentum P_T of the
produced B_c and B_c^* is much larger than the mass of the B_c meson.
