  We study flavor changing processes $\Upsilon \to B/{\bar B} X_s$ and $J/\psi
\to D/{\bar D} X_u$ in the B factories and the Tau-Charm factories. In the
standard model, these processes are predicted to be unobservable, so they serve
as a probe of the new physics. We first perform a model independent analysis,
then examine the predictions of models; such as top color models and MSSM with
R-parity violation ; for the branching ratios of $\Upsilon \to B/{\bar B} X_s$
and $J/\psi \to D/{\bar D} X_u$ . We find that these branching ratios could be
as large as $10^{-6}$ and $10^{-5}$ in the presence of new physics.
