RBS, owner of Ulster Bank, is cutting 221 technology jobs in Dublin and Belfast. Meanwhile, Lloyds Banking Group says it is closing its Black Horse personal loan centres and axing 585 roles.
RBS, majority owned by the UK government, is closing down its IT operations in Ireland by the autumn, costing 196 jobs in Dublin and 25 in Belfast because the "roles are no longer required".
Some positions will be moved to other back office hub locations in the UK and elsewhere, says the bank in a statement.
The losses are part of plans outlined in April to cut 9000 jobs worldwide at the bank in a bid to save £2.5 billion over three years.
The Irish Bank Officials' Association (IBOA) union says it has met the affected staff and asked RBS to review its position.
Larry Broderick, general secretary, says: "While IBOA acknowledges management's commitment to negotiate with the Union about these job losses on a voluntary basis, it is clear that unless RBS provides alternative IT job opportunities in Ireland, these redundancies will to all intents and purposes be compulsory."
Separately, Lloyds Banking Group says the closure of its Black Horse personal finance centres in the UK will cost 455 jobs. Another 130 positions will be lost at the bank's retail arm.
The Unite union says it is "deeply disappointed" by the news, warning Lloyds "not to repeat the disastrous strategies of 2009 which brought over 15,500 job losses".