Athletic Club, FC Internazionale Milano and Liverpool FC are in charge of their respective third qualifying round ties, but nervy second legs are in store for a couple of established names.
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Some big names are in danger of tumbling out of the UEFA Europa League when the third qualifying round concludes on Thursday.
One famous team at risk of not reaching the play-offs is FC Steaua Bucureşti, the 1986 European champions having been shocked in the first leg by FC Spartak Trnava. The Slovakian side lead 1-0 thanks to Martin Mikovič's early goal at the National Arena, venue for last season's final.
The outlook is particularly bleak for Steaua's city rivals, FC Rapid Bucureşti. Ioan Ovidiu Sabau's charges lost 4-0 at sc Heerenveen and so require a dramatic turnaround if they are to remain on course to repeat their group stage appearance of last term.
Legia Warszawa, who reached the round of 32 in 2011/12, are also up against it following a 2-1 defeat by SV Ried, though Danijel Ljuboja's late goal gives them hope going into the second leg in the Polish capital.
Slightly better placed, but still with work to do, are Olympique de Marseille, who were held 1-1 in Turkey by Eskişehirspor. FC Dinamo Moskva, meanwhile, will be confident of progressing after Aleksandr Kokorin's 93rd-minute goal secured a 2-2 draw at Dundee United FC.
A number of clubs who went far in last season's edition are well set to overcome the first hurdle in their path to the Amsterdam ArenA, the stage for the 2013 showpiece. Losing finalists Athletic Club will defend a 3-1 lead at NK Slaven Koprivnica, Hannover 96 hold a 3-0 advantage over Saint Patrick's Athletic FC, while FC Twente and FC Viktoria Plzeň are both two goals to the good ahead of their respective returns against FK Mladá Boleslav and Ruch Chorzów.
There should be few problems for 2010 UEFA Champions League winners FC Internazionale Milano following their 3-0 defeat of HNK Hajduk Split. Liverpool FC, three-time UEFA Cup victors, welcome FC Gomel to Anfield for Brendan Rodgers' first home game in charge leading 1-0.
A full list of Thursday's 29 second-leg matches is available here.