  We present factorization theorems for two exclusive heavy-quarkonium
production processes: production of two quarkonia in e^+e^- annihilation and
production of a quarkonium and a light meson in B-meson decays. We describe the
general proofs of factorization and supplement them with explicit one-loop
analyses, which illustrate some of the features of the soft-gluon
cancellations. We find that violations of factorization are generally
suppressed relative to the factorized contributions by a factor v^2m_c/Q for
each S-wave charmonium and a factor m_c/Q for each L-wave charmonium with L>0.
Here, v is the velocity of the heavy quark or antiquark in the quarkonium rest
frame, Q=sqrt{s} for e^+e^- annihilation, Q=m_B for B-meson decays, sqrt{s} is
the e^+e^- center-of-momentum energy, m_c is the charm-quark mass, and m_B is
the B-meson mass. There are modifications to the suppression factors if
quantum-number restrictions apply for the specific process.
