The Opposition parties congratulated the Mr Ahern on his re-election as Taoiseach but question whether his Government would be stable enough to last the full term.
The Fine Gael leader Enda Kenny warned that Mr Ahern's new Government would not be a compatible one.
He said: "While I congratulate the Cabinet and wish them well personally, it is my duty to say that what we are witnessing today in this government, is not the marriage of true minds.
"What we are witnessing today is the ultimate, cynical marriage of convenience.
"It is broad-based yes but it most certainly is not compatible."
Mr Kenny went on to say that the Fianna Fáil "bicycle" now how two mudguards to help protect it, "at the front the well-used but badly-worn PDs at the rear the eager Greens all shiny and new".
He also said the "bicycle" was supported by "three stabilisers, bought off in secret deals with the taxpayers' money".
The Labour Party leader also welcomed the new Cabinet and said it was a "privilege" but he attacked the Green Party by saying they are only "guests" in power in a "dolly mixture" of a Government.
Mr Rabbitte asked whether a government with "two diametrically opposed parties, both with acting leaders, and a third party with the Leader on the way out" is this the best type of government to confront the economic challenges ahead?
Sinn Féin Dáil Leader Caoimhghín Ó Caoláin said his party would not be supporting a Cabinet and a Programme for Government which is set to continue the "failed policies" of the previous Fianna Fáil Progressive Democrats government.
Mr Ó Caoláin went on to say the negotiation of the Programme for Government had "exposed the myth" that there is any difference between Fianna Fail and the PDs.
"Fianna Fáil seems to have negotiated on behalf of the PDs. The Green Party has been co-opted as an insurance policy but they may well find themselves sharing the same fate" he added.