McClaren's side face a testing task
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Middlesbrough will face Italian giants Lazio in the new Uefa Cup group format, along with Spain's Villarreal, Partizan Belgrade and Greek unknowns Egaleo.
Newcastle have been drawn alongside Sporting Lisbon, Sochaux, Panionios and Dinamo Tbilisi of Georgia.
Rangers play Auxerre of France, Grazer AK of Austria, Poland's Amica Wronci and Dutch side AZ Alkmaar.
Scottish counterpart Hearts face Ruud Gullit's Feyenoord, Schalke 04, Basle, and Millwall's conquerors Ferencvaros.
Boro and Newcastle will open their campaigns in Greece on the same night but Uefa does not expect security to be an issue.
Spokesman Rob Faulkner told BBC Radio Five Live: "We reviewed the situation at the beginning of the season.
"We've been in contact with the Greek FA and we've got assurances from them that it's not a problem.
"There's about 50km distance between the two locations so both those matches can go ahead."
Under the new set-up, Middlesbrough will play Egaleo away before facing Lazio at the Riverside. They will then visit Villareal before ending the group with a home game against Partizan.
Newcastle face Panionios before Dinamo Tbilisi visit St James' Park. Graeme Souness's side then travel to Sochaux before a potentially key home fixture against Sporting Lisbon.
Hearts have a tough opener at Feyenoord before they play Schalke at home. Craig Levein's side then face Basle in Switzerland before ending the group at home to Ferencvaros.
Rangers start in Poland against Amica Wronki before AK Graz come to Ibrox. They then travel to AZ Alkmaar ahead of a home game against Auxerre.
Middlesbrough are playing in Europe for the first time after winning their first major trophy - the Carling Cup - last season.
Newcastle may face a reunion with midfielder Hugo Viana, who has returned to the Portuguese capital on loan after his £8.5m move from Sporting to Tyneside flopped.
The Magpies made comfortable progress against Israeli side Hapoel Bnei Sakhnin in the last round, winning 5-1 in Tel Aviv for a 7-1 aggregate win.
They reached the semi-finals last season before being eliminated by a Marseille side inspired by Chelsea's summer recruit Didier Drogba.
Rangers defender Jean-Alain Boumsong will face his former club in Auxerre, while Fernando Ricksen also played for Alkmaar.
Each club will play two matches at home and two away on the following dates: 21 October, 4 November, 25 November, 1/2 December and 15/16 December.
The winners, runners-up and third-placed clubs from each group will advance to the last 32 where they will then be joined by the eight third-placed clubs from the Champions League group stage.
The competition will then revert to a two-leg knock-out format.
The final will be played in Lisbon's Jose Alvalade Stadium on 18 May 2005.
The draw in full.
Group A
Feyenoord, Schalke 04, Basle, HEARTS, Ferencvaros.
Group B
Parma, Besiktas, Athletic Bilbao, Steaua Bucharest, Standard Liege.
Group C
Club Brugge, Real Zaragoza, Utrecht, Dnipro, Austria Vienna.
Group D
NEWCASTLE, Sporting Lisbon, Sochaux, Panionios, Dinamo Tblisi.
Group E
Lazio, Villarreal, MIDDLESBROUGH, Partizan Belgrade, Egaleo
Group F
RANGERS, Auxerre, Grazer AK, Amica Wronki, AZ Alkmaar
Group G
Vfb Stuttgart, Benfica, Dinamo Zagreb, Heerenveen, Beveren.
Group H
AEK Athens, Lille, Sevilla, Alemania Aachen, Zenit St Petersburg.
The first match day will be on 21 October.