Two men have been charged following the Aberdeen v Rangers game on Sunday.
A 25-year-old, from Aberdeen, has been charged in relation to an offence involving possession of pyrotechnic and 22-year-old man, from Glasgow, has been charged regarding offensive behaviour within a football stadium.
Reports have been sent to the Procurator Fiscal.
Police have also launched an investigation after a Rangers bus was vandalised in the early hours of Sunday morning in the Deeside area.
Enquiries are ongoing and anyone with information is urged to contact Police Scotland.
Chief Superintendent Thomson said: "As anticipated the vast majority of fans who attended Pittodrie on Sunday acted in a safe and responsible manner which assisted officers in ensuring the safety of those in attendance and the wider public.
"I would like to take this opportunity to thank them for their support.
"In saying this, and despite repeated warnings from Police Scotland in the lead-up to match, I am extremely disappointed that a very small minority of fans chose to conduct themselves in an anti-social and completely unacceptable way.
"I understand that feelings run high at these events, however such behaviour is inexcusable.
"It also creates significant security issues which put your own safety and the safety of others at risk.
"For those who have committed offences and were not detected at the time I can assure you that you will face the consequences of your actions.
"Retrospective enquiries are being carried out and we have a dedicated team working in partnership with both clubs to identify those people in the stadium and outwith who let not only themselves down but their clubs too.
"I would appeal to anyone with any information about any of the incidents in question that could help with our inquiries to contact Police on 101 or Crimestoppers if you would prefer to remain anonymous on 0800 555111."
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