The Hearts defenders, Craig Levein and Graeme Hogg, have been disciplined by the club for exchanging punches in a pre-season friendly and, given their 2-0 defeat by AEK Athens in the European Cup in midweek, Rangers are beginning to realise that, however big they have become in Scottish and even British terms, the success they so covet in Europe continues to elude them.
The standing of Scottish football in Europe is so low that three clubs have been involved in preliminary ties this week, with only Motherwell recording a win in their first leg, and that against the amateur side, HB Torshavn, of the Faroe Isles.
Last term, the Ibrox club retained the strength to continue to dominate the domestic league although, despite his summer signings of Brian Laudrup and Basile Boli, Walter Smith, the Rangers manager, remains cautious.
'It's difficult for us every season and I don't agree with the statement that it's a foregone conclusion that Rangers will win things. We have to pick ourselves up from the European disappointment and start to boost our own confidence by playing as we can.'
The demands of the Taylor report have forced clubs to concentrate on building stands rather than squads, reducing the amount of transfer activity from those who would wrest the League crown from Rangers' grasp, with Aberdeen likely to provide the greatest challenge.
Willie Miller, their manager, has made three signings, breaking the club transfer record by bringing Billy Dodds, the striker from St Johnstone, for pounds 800,000, and also adding Peter Hetherston from Raith Rovers and Colin Woodthorpe from Norwich. The test of Miller's side will come not from their encounters with the Old Firm but in the matches against the smaller sides they will be expected to beat.
Celtic approach the season with more confidence than they have dared for the last few years with Tommy Burns, their former player, in the manager's chair. Already, in pre-season games, his players have provided evidence that the spirit has returned to a squad which had been drained by constant boardroom squabbles.
The title might prove beyond their means, but Burns will be hopeful that a trophy can be won after a gap of five years. 'Some of the players here have been allowed to forget how good they are, and they could surprise a few people, including themselves, this season,' he said.
Three clubs, Partick Thistle, Kilmarnock and Falkirk, are expected to contest the one automatic relegation spot from the Premier Division while, on the international front, Craig Brown, the Scotland manager, knows he faces an important year of European qualifying matches which will go a long way to deciding his future.