They take on Albanian and Dutch opponents, respectively.
Dundalk manager Vinny Perth says his squad have grown in confidence after last week's win in Europe.
They knocked out Levadia Talinn to set up a third qualifying round tie in the Europa Conference League against Dutch top-flight side Vitesse Arnhem.
The Lilywhites are away from home for the first leg tonight.
Shamrock Rovers have a great chance to bounce back from their Champions League elimination.
The defeat to Slovan Bratislava just over three weeks ago saw the Hoops drop into the Conference League.
The Premier Division champions' third-round first leg is against Teuta of Albania.
Kick-off at Tallaght Stadium is at 8pm.
Celtic are at FK Jablonec in Europa League qualifying.
There's a quarter-to-five kick-off in the Czech Republic.
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