Hall measurements using continuous extremely slow cooling and reheating rates as well as employing eqiulibrium point‐by‐point conventional techniques reveals a clear anomally inRHat pre‐onset temperatures nearTcin polycrystalline samples Y1Ba2Cu3O7and Bi2Sr2Ca2Cu3O10. The anomaly has the appearance of a singularity of Dirac‐delta function which parallels earlier work on La1−xSrxCuO4. Recent single crystal work on the Bi‐containing high‐Tcsuperconductor is in accord with a clearcut anomaly. The singularity is tentatively interpreted to be associated (upon cooling) with initially the removal of positive holes from the hopping conduction system of the normal state such as from the increased concentration of bound virtual excitons due to increased exciton and hole lifetimes at low temperature. Subsequently the formation of Cooper pairs by mediation from these centers (bound‐holes) and/or bound excitons) may cause an ionization of these bound virtual excitons thereby re‐introducing holes and electrons into the conduction system atTc.