The Dons are in Tbilisi to face Georgian side Chikhura Sachkhere in their first-leg tie, with the return match at Pittodrie next week.
Derek McInnes' side beat RoPS 4-2 on aggregate in round one and are looking to secure a third-round meeting with Rijeka of Croatia.
Rangers thumped St Joseph's 10-0 on aggregate to set up a clash with Progres Niederkorn of Luxembourg. Steven Gerrard's men, who are at home in the first leg, will play Danish outfit Midtjylland should they go through.
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