A total of 135 amendments to the NAMA legislation have been submitted for consideration during the Report Stage of the debate, which is being held today and tomorrow.
The debate has adjourned for the night and will resume tomorrow morning.
The Report and Final Stages of the legislation are due to finish in the Dáil tomorrow evening at 8pm.
Further amendments are expected to be proposed by Minister for Finance Brian Lenihan in the Seanad when the Upper House begins its consideration of the legislation next week.
The first amendment is a Sinn Féin one calling for the NAMA bill to be titled in Irish only.
It calls for the bill to be titled An Bille fán nGníomhaireacht Náisiúnta um Bainistíocht Sóchmhainní 2009.
Proposing amendment number two, Fine Gael's Finance Spokesman Richard Bruton said there is a need for an Oireachtas Committee to 'keep an eye on' NAMA and 'to ride shotgun' on the performance of the agency.
Deputy Bruton's amendment would allow the committee to vet members of the NAMA board, monitor and review NAMA's work, and to require staff members of NAMA to come before it.
It also calls for an Opposition member to be appointed to chair the committee.
Mr Bruton also said that the Special Purpose Vehicle must be regulated by the NAMA legislation.
The Special Purpose Vehicle will manage and dispose of assets and will be privately controlled.
Green Party TD Paul Gogarty asked the Minister for Finance to support the Fine Gael amendment on making the SPV more transparent.
Proposing her party's amendment for an oversight committee, Labour's Joan Burton said a key lesson from dealing with banking crises around the world shows that unless high transparency and oversight is part of the exercise, bankers will run back and start to do the same things that led to the crash in the first place.
