The Scottish Professional Football League is to investigate incidents of "unacceptable conduct" at Ibrox and Tynecastle last month.
A statement from the governing body said there will be a review of crowd behaviour at Rangers v Hibernian and Hearts v Dundee United.
Following the match at Ibrox on 28 December, Rangers condemned "a minority" for "inappropriate singing".
At Tynecastle two days later, there were reports of segregation problems.
The SPFL statement does not outline any details but makes reference to match delegate reports.
"The SPFL is committed to addressing unacceptable conduct where it occurs," it reads.
The announcement comes 24 hours after the SPFL revealed it had set up a working group to examine problems relating to anti-social behaviour from fans.