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2 February 2015, 12:36 | Updated: 2 February 2015, 12:39
37 people were arrested as thousands of fans attended the first Old Firm clash in almost three years.
Police said the vast majority of fans at the League Cup semi-final match between Rangers and Celtic were well-behaved.
A total of 19 people were detained at Hampden Park, and another 18 across the city. 12 were for alleged sectarian breaches of the peace.
Tensions were high at what was the first game between the clubs since Rangers' liquidation in 2012.
Celtic eased to a 2-0 victory amid a large police presence at the stadium.
Officers were also deployed in Glasgow city centre and at major transport hubs before, during and after the match.
Event commander Chief Superintendent Andy Bates, said: "As usual the vast majority of the 50,000 fans were here to enjoy the game and support their respective team; they deserve credit for their excellent behaviour.
"However, again, it is the minority of fans who spoiled the occasion by for example setting off flares and singing sectarian songs.
"We dealt with any incidents swiftly and with minimum disruption.
The sell-out game had an international television audience in 54 countries.
The Scottish Professional Football League said it had a potential audience of 129 million outside of the UK, with broadcasters in the US, Australia, Europe and Asia screening it.
Celtic will now meet Dundee United who beat Aberdeen 2-1 in the first semi-final at Hampden yesterday.