Rangers are looking to forget Wednesday's Champions League stalemate whilst Celtic are upbeat after their European victory going into today's Scottish Premiership matches.
Rangers travel to Aberdeen, who held them to a draw on their last league visit to Pittodrie, and Celtic are eager get a victory under their belts against visitors Dundee United.
The Gers go to the Granite City on the back of a frustrating 1-1 draw at Ibrox in the Champions League final qualifying round against FC Copenhagen, and manager Alex McLeish is looking for an improved show.
"It will take a much better performance from several of the players," McLeish told the club's official Web site.
"But the players themselves know that they can give more in certain positions and I'm looking for that improvement."
Rangers swatted away a recent approach for club captain Barry Ferguson from former Gers boss Graeme Souness, now managing English side Blackburn Rovers.
"We've made an enquiry for Barry in the last seven days but we were told he's not for sale," Souness told the Lancashire Evening Telegraph.
Rangers are short on cash but Rovers are likely to accept no for an answer.
The Gers brought in a handful of cut-price players during the close season, but only Georgian defender Zura Khizanishvili has so far started a game.
New signings Henning Berg, Paolo Vanoli and Nuno Capucho may be in the first 11 against Aberdeen after sitting on the bench midweek.
Meanwhile, Celtic got their Champions League campaign off to a flying start with a 4-0 win over MTK Hungaria in Budapest.
But domestically, the Bhoys are already two points behind their Old Firm rivals, having drawn a blank at Dunfermline last Saturday.
Manager Martin O'Neill is still without suspended striker Chris Sutton, but Sweden midfielder Johan Mjallby may feature against Dundee United after skipping the Hungaria and Dunfermline matches with a knee problem.
"He trained, and you know what Johans like -- he'll want to go through with it anyway," said O'Neill.
"But he said he was feeling about the same as he did on Saturday, so we thought best to leave him out."
Hearts travel to Hibernian in the Edinburgh derby, with both teams going into the clash in form.
Hibs staged a second-half comeback to beat Dundee United 2-1 away last Saturday, whilst the Jam Tarts sent Aberdeen home with a 2-0 defeat.
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