Gleeson senior has been nominated for his role as a troubled priest in Calvary, while his 30-year-old son is up for the same prize for his turn in Richard Curtis' romance About Time. They face competition from Ciaran Hinds (The Sea) and Andrew Scott (The Stag).
Calvary is also up for the Best Film trophy, alongside Byzantium, The Stag, Run & Jump and The Sea, while Saoirse Ronan (Byzantium), Antonia Campbell-Hughes (3096 Days), Jane MCGrath (Black Ice) and Kelly Thornton (Life's A Breeze) will battle it out for Best Actress.
Big names make up the Best Supporting Actor category. Colin Farrell and Michael Fassbender are nominated for their respective roles in Saving Mr. Banks and 12 Years A Slave, alongside Edward MACLiam (Run & Jump) and Peter MCDonald (The Stag).
Sinead Cusack (The Sea), Fionnula Flanagan (Life's A Breeze), Amy Huberman (The Stag) and Orla O'Rourke (Calvary) will compete for the Best Supporting Actress prize.
The winners will be announced at a ceremony in Dublin, Ireland on 5 April (14).