McAvennie made a slow start at Celtic and his progress was not helped when he got involved in an on-field fracas with Chris Woods, Terry Butcher and Graham Roberts in an Old Firm game in November 1987. McAvennie and Woods were sent off in the initial incident, whilst Butcher was sent off later in the game. All four were later reported to the Procurator Fiscal and appeared in court on disorder charges relating to their conduct in that game. McAvennie was found not guilty, Roberts not proven, whilst Butcher and Woods were both convicted of Breach of the Peace.