I have been trying to find any records for two of my families from Kremenchug or environs.
My understanding is that the records were actually destroyed during the Second World
War. There is a story on JewishGen by a father and son's research trip to Kremenchug who report ed the above.
If there is any information to the contrary I would be very happy to let you know via the JewishGen discussion group or to you directly.
Researching: Asovich/Asowitch, Skolnik/Skolnick- Kremenchug, Poltava