Carlos Tevez and Gary Neville, the two central figures in the acrimony that has surrounded this season's Manchester derbies, will be under police orders not to do anything that could incite crowd trouble when City and United renew hostilities tomorrow.

Greater Manchester police, planning one of the biggest football operations of the season, are to speak to both clubs to emphasise the importance of the two sets of players behaving responsibly rather than fuelling existing tensions.

The police are anxious about the way the players celebrate goals, and it will be made clear to the two clubs that this should not involve deliberately goading opposition supporters.

When United beat City at Old Trafford with an injury-time goal in September the United captain Neville, an unused substitute, ran along the touchline to celebrate provocatively in front of the away end. The Football Association subsequently wrote to Neville to warn him about his future conduct but the former England player was involved in more controversy in the first leg of the Carling Cup semi-final in January, when he flashed his middle finger at Tevez after his former team-mate had scored from the penalty spot.

Tevez had gestured towards Neville after running to celebrate in front of Sir Alex Ferguson's dugout and, still nursing a grievance from the way he perceives he was treated at Old Trafford, cupping his ears towards United's officials in the directors' box. The striker subsequently called Neville a "boot-licker" and a "moron" in an interview on Argentinian radio, an outburst that led the police to contact his club because of their concerns that he was fuelling the potential for trouble.

Eighteen people were arrested before, during and after that encounter at Eastlands and police confiscated items including darts and golf balls from United's fans. Other objects were thrown on to the pitch by both sets of supporters, including a cigarette lighter that struck the United left-back Patrice Evra.

Roberto Mancini, the City manager, has been warned and fined £20,000, suspended until the end of the 2011-12 season, after admitting misconduct following his touchline clash with David Moyes during his side's home defeat to Everton last month.