Price will fancy his medal chances if he gets past Timurziev
Several of Britain's boxers have been handed tough opening bouts in an unseeded draw at the Beijing Olympics.
Super-heavyweight and team captain David Price will face Russia's European champion and world number one Islam Timurziev on Wednesday.
Middleweight James Degale beat Egypt's Mohamed Hikal in his opener, but will probably have to defeat Russian world champion Matvei Korobov to win a medal.
GB have already been hit by Frankie Gavin's withdrawal ahead of the Games.
The world amateur lightweight champion returned home after failing to make the weight.
Head coach Terry Edwards said Gavin had rung him to wish the team well, but they were given no favours in the draw.
"The draw has not been kind to us," he admitted. "All the team have proved they can beat the best in the world and they will have to do it again."
Hikal is a former African champion and two-time Olympian but Degale got his team off to a winning start on Saturday.
North-East pair Bradley Saunders and Jeffries received the kindest draws.
Light-welterweight Saunders opens against Ghana's Samuel Kotey with his biggest obstacle to a medal likely to be Bulgaria's European champion Boris Georgiev in the last eight.
Jeffries starts with a bye and if he defeats Colombia's Pan-American champion Eleider Alvarez on Thursday and, in all likelihood, classy Hungarian Istvan Szello - whom he has already beaten - he will be guaranteed at least bronze.
Flyweight Khalid Yafai begins in the second round against Cuban Andry Laffita on Tuesday, while welterweight Billy Joe Saunders faces Turkey's world number three Adem Kilicci on Sunday, with another Cuban awaiting in round two.
Meanwhile young bantamweight Joe Murray must open on Tuesday against China's fancied Yu Gu, whom he beat in November's World Championships, in front of what is expected to be a fervent 13,000-strong home crowd.
Belfast light-flyweight Paddy Barnes starts with a bye and can certainly be confident of reaching the medal stages, while fancied middleweight Darren Sutherland drew Nabil Kassel of Algeria.