El-Hadji Diouf and Madjid Bougherra have escaped without further bans for their part in last month's Old Firm derby but have been fined and warned over their future conduct by the Scottish Football Association.
The Rangers duo faced the SFA's disciplinary committee on Tuesday to answer a case of "misconduct of a significantly serious nature" as a result of their actions during the Scottish Cup replay on March 2.
Diouf was fined £5,000 by the governing body, while Bougherra was fined £2,500. Both players were red-carded in the match.
Diouf and Bougherra, along with team-mate Steven Whittaker, were shown red cards in the 1-0 defeat at Celtic Park, with those automatic suspensions coming into effect in next season's competition.
On-loan Blackburn player Diouf was cautioned for clashing with Celtic boss Neil Lennon on the touchline, before earning a red card for dissent after approaching referee Calum Murray after the final whistle.
Instead of leaving the pitch, he then made his way to the Rangers fans and threw his shirt into the crowd.
Bougherra was dismissed deep into injury time for a second bookable offence and grabbed the match official's arm in an attempt to prevent him from showing his cards.
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