The day's discussions are expected to start with amendments to Clause 11 which gives 'legislative competence to the Scottish Parliament in relation to the regulation of air weapons'.
Following amendments will focus on the Scottish Parliament's role in insolvency procedures and managing health professionals.
If time allows, Lords may discuss the prospect of Scotland having its own time zone in Amendment 23.
Catch up on committee stage day one
The committee day started with a two and a quarter hour debate over Lord Forsyth of Drumlean's (Conservative) motion to postpone the bill pending a further legislative consent motion from the Scottish Parliament and the results of a Government consultation.
His motion suggested that the house: 'declines to consider the bill in Committee until Her Majesty’s Government have laid before Parliament a report on the results of the consultation they launched on 11 January on Scotland’s constitutional future and until the Scottish Parliament has passed a further Legislative Consent Motion in respect of the bill.'
He withdrew the amendment saying: 'It is fantastic that we have had such a turnout given that the debate was scheduled for the Thursday after Burns Night when many of us would have been in Scotland and perhaps not as bright and breezy as people obviously were this morning.'
Lords continued the session looking at the function of Scottish Parliament and whether Clause One, covering the administration of elections, should remain part of the bill.
Lord Browne of Ladyton (Labour) outlined his view that the debate: 'The purpose of this opposition to Clause One standing part of the Bill is to probe what appears to be a selective implementation by the Government of the Calman commission's recommendations.'
The amendment was withdrawn after reassurance from the Advocate-General for Scotland Lord Wallace of Tankerness (Liberal Democrat). He said: 'There is no corresponding widening of the legislative competence of the Scottish Parliament although, obviously, it will have a role in approving the subordinate legislation made by Scottish Ministers. So it is executive devolution rather than legislative devolution. Specifically, Scottish Ministers will be able to make provision by order as to the conduct of Scottish Parliament elections, the questioning of such an election and the consequences of irregularities.'
The previous stage (Second Reading) took place on 6 December 2011.
What is the committee stage?
During committee stage, detailed line-by-line examination of separate clauses and schedules of the bill takes place. Any member of the Lords can take part. It can last for one or two days to eight or more. This stage usually starts no fewer than two weeks after the second reading.
The day before committee stage starts, amendments (proposals for change) are published in order in a Marshalled List. Amendments on related subjects are grouped together and a 'groupings of amendments' is published on the day. Lords must agree to every clause of the bill and vote on the amendments. All proposed amendments can be discussed and there is no time limit for discussion.
After the committee stage, the bill is reprinted with all the agreed amendments and is moved to report stage for further examination.