Flavor-Changing Neutral Current Constraints in Topcolor-Assisted Technicolor

It is argued that the topcolor models recently proposed by Hill [1] may face significant constraints from flavor-changing neutral current processes (such as $B-\bar{B}$ mixing) unless the mixing angles between down-type quarks are small. The flavor-changing processes are mediated by scalar bound states which are likely to be light as a result of the near critical dynamics of the $b$-quark sector. The consequences of the latter on the bottom quark mass are also briefly discussed.