While there may not be any adoption records there may be a guardianship set up for the children. This is more likely if there was any money in the biological parent's estate.
Look in the Guardianship records or administrative records for the probate court. Don't forget the accounting records where trust etc. were monitored and closed out.
You may find some clues in the will of the people who adopted the children.
I have just completed a project to find information on the adoption of a 2nd great grandfather.