Carmarthen Town will be away to Irish side Longford in the first leg of their first qualifying round Uefa Cup tie.
CSKA Moscow lifted the Uefa Cup last season
Rhyl, who are at home in the first leg, have been handed one of the longest possible journeys in the northern group after drawing Lithuanian side Atlantas.
The ties will be played on 14 and 28 July, with the winners going through to the second qualifying round.
The 31 teams who progress from the second qualifying round will join 49 more teams in the first round proper.
Carmarthen's tie with Longford will be only the second meeting between a Welsh and Irish club in European competition.
Longford Town, currently sixth in the Eircom League, qualified as winners of their domestic cup while Carmarthen were losing finalists to double winners TNS.
Rhyl's opponests Atlantas are third in the Lithuanian national league and have lost heavy in all of their previous Uefa Cup ties.