NICOLA Sturgeon has admitted she could face a "particular challenge" from an influx of new members wanting to hold another referendum on independence sooner than she does if she becomes SNP leader.

The Deputy First Minister, who has no plans for a fresh referendum, said if the members and leadership were out of step it could cause issues for "the next couple of years".

However, Sturgeon - who is almost certain to succeed Alex Salmond unopposed as SNP leader and First Minister in November - said she would far rather deal with this issue than the exodus of members she believes is facing Labour.

Since the No vote, all the parties which were part of the Yes campaign have experienced an unprecedented surge in membership applications from people wanting to carry on the fight for independence.

Membership of the Scottish Greens jumped from 1720 on polling day to 6235 by last Friday, while the Scottish Socialist Party has grown from just more than 1000 to a record 3600.

The SNP, which had about 25,000 members before September 18, has more than doubled and could soon triple in size, becoming the third largest party in the UK, above the Liberal Democrats. Its membership yesterday was more than 68,200.

Speaking to the Sunday Herald, Sturgeon said it was too early to tell what new members wanted, but their sheer number - equivalent to 1% of Scotland's electorate - would "undoubtedly change the SNP … to something much closer to a genuine grassroots, community-based campaigning force".

After the intense emotions of the referendum, she said the challenge for the SNP would be "to make sure these people don't get disillusioned or feel a few months down the line that they've lost some of that enthusiasm".

She said: "I'm sure a lot of the people who have joined will not have a huge appetite for sitting through endless branch meetings, but that's an inevitable part of democracy.

"We as an organisation have to be willing to adapt. We need to look at our structures, we need to look at our ways of doing things as a party, and make sure that they are fitting for something that is a much bigger, more diverse, more grassroots organisation."

Sturgeon said last week that the timing of another referendum on independence would be determined by circumstances and the public mood for one, rather than according to a fixed timetable.

She said new members were "impatient for change" but also realistic about accepting a No vote.

Asked if she was worried about members wanting to return to the referendum issue at a quicker pace than the leadership, she said: "That's always going to be a challenge of leadership and it's a particular challenge with such a big group of new members.

"But I would rather - with all the issues that might give me to deal with if I am leader over the next couple of years - I would far rather be in that position than be in the position which Labour must be in, of watching members leave.

"Every scenario brings its own difficulties and challenges, but this is a far more positive one to be ­dealing with."

In 2013, the average age of an SNP member was 53, with only 10% under 30 and 25% aged over 65. Just 33% of party members were women.

The new intake is expected to both lower the average age of members and increase the proportion of women. On a practical level, the party will soon outgrow its usual conference venue in Perth, and from next spring it will be too big to meet anywhere except Glasgow or Edinburgh.

However, the most profound change could be in political attitude, with many recruits impatient for a new referendum, many further to the left than the SNP at present, and many unwilling to take orders from a centralised party HQ.

"The discipline is gone," said one senior Yes campaigner, who said the new recruits were at least united in hating Labour and wanting to kill it as a political force in Scotland.

Dr Duncan Ross, a former SNP National Secretary, said the influx was welcome but that the SNP faced a challenge "to maintain a clear political identity that is not just the Yes coalition".

He also said the SNP may now shift to the left.

"There may be pressure to move that way. We will see over six months to a year how strong that becomes. The party is the membership."

As to the timing of another referendum, Dr Ross, who is convener of the SNP's Glasgow Kelvin Association, said: "My own view is, we would be crazy to go into 2016 with a referendum in our manifesto, unless circumstances change dramatically.

''You have to accept the outcome. You can't keep digging this up. You move on. There's a big battle for home rule to be fought."