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Kilmarnock have been drawn against Belgian side Cercle Bruges in the Europa League second qualifying round.
Derek McInnes' side will host the first leg on 25 July before visiting Belgium a week later.
Stephen Robinson's St Mirren will find out their Europa Conference League opponents when the draw is made at 13:00 BST.
Kilmarnock, who finished fourth in the Scottish Premiership and last played in European competition in 2019, had been unseeded in Wednesday's draw and could also have been paired with Ajax, Molde, Rapid Vienna or Trabzonspor.
Cercle Bruges were the least experienced of those potential opponents in European competition.
They have qualified for only the fourth time and for the first time since reaching the Europa League third qualifying round in 2011, when they lost to Anorthosis Famagusta.
Led by 41-year-old Miron Muslic, the Bosnian who stepped up from assistant in 2022, they finished fourth in the Belgian Pro League last season.
Should Kilmarnock win, they will have to negotiate a third qualifying round, where they would again be unseeded, and a play-off round if they are to reach the group stage.
If the Belgians win, Kilmarnock will drop into the Conference League third qualifying round as an unseeded side.
St Mirren, who were fifth in the Premiership and whose most recent European involvement dates back to 1987, are seeded in the Conference League second qualifying round draw.
They will face Brann, Hacken, Cliftonville or the winner of the ties between Magpies and Derry City, or Valur and Vllaznia.
Should St Mirren progress, they would also face a third qualifying round and a play-off to reach the group stage.