Angus Robertson, Moray MP, is the early favourite, already the party’s Westminster leader and the most experienced in parliamentary terms of the contenders, having been an MP since 2001.
Tommy Sheppard, has been an MP, for Edinburgh East since 2015, has a journey that mirrors many of the new SNP members who joined during and after the independence referendum.
A former Labour Party Assistant general Secretary in the 1990s he became disillusioned with the party and eventually joined the SNP in 2014.
Alyn Smith, has been an MEP since 2004 and has been active since the EU referendum gathering support in the European Parliament Brussels and Strasbourg for Scotland to remain when the UK leaves.
Chris McEleny, is a West Dunbartonshire councillor from the left of the party looking to win support from fellow councillors and local government activists.
The new deputy will have responsibility for a fresh bid to convince Scotland of the benefits of independence.
Mr Robertson said a future independence campaign will have to address the “potential downsides” of independence.
He said: “I think it is incumbent on politicians of all political persuasions to say that not everything is going to be easy and, of course, establishing a sovereign state is a big step, and I think we need to be clear with the electorate and that’s why part of my pitch in this SNP depute leadership election campaign is that I think we need to be outward-focused.”
He said the party had to target all voters and particularly the no voters who were not convinced.
He added: “For some of them, the reason why they weren’t convinced was they thought that the explanation of why independence was a good thing didn’t concede that there were potential downsides and, of course, if one takes responsibility for oneselves it is entirely possible that one makes bad decisions, that there are downsides to things.”
The party membership of around 120,000 will have a vote in the contest with hustings starting as early as next week before the deputy leader is announced at the Annual Conference in Glasgow in October.