Police Scotland have opened an investigation after complaints were made around donations to the SNP.
It follows allegations that £600,000 raised for campaigning towards Scottish independence was diverted elsewhere.
Nicola Sturgeon has previously denied any money has gone missing, saying the party’s finances have been independently audited.
Two SNP MPs quit the ruling National Executive Committee (NEC) in May, citing a lack of transparency from the party.
At that point, Police Scotland said they were assessing a fraud allegation relating to £600,000 of funds “to determine if an investigation is required”.
We will now carry out an investigationPolice Scotland
On Tuesday, a spokeswoman said: “Police Scotland has now received seven complaints in relation to donations that were made to the Scottish National Party.
“After assessment and consultation with the Crown Office and Procurator Fiscal Service, we will now carry out an investigation.
“Inquiries are continuing and anyone who has any information which may assist with this investigation is asked to contact police.”
The force has not stated exactly which donations the investigation relates to.
In May, MPs Douglas Chapman and Joanna Cherry resigned from the NEC.
Mr Chapman had been the party’s national treasurer and said he had not been given enough information to do his job.
On Twitter, he said: “Despite having a resounding mandate from members to introduce more transparency into the party’s finances, I have not received the support or financial information to carry out the fiduciary duties of National Treasurer.
“Regretfully, I have resigned with immediate effect.”
The SNP’s business convener Kirsten Oswald said she “fundamentally disagreed” with this description.
In June, the First Minister told STV News: “I’m not concerned about the party’s finances.
“The finances of the SNP are independently audited, our accounts are sent to the Electoral Commission in common with other parties and of course published, so there’s full scrutiny around that.
“Money hasn’t gone missing. All money goes through the SNP accounts independently and fully audited.
“We don’t hold separate accounts, we’re under no legal requirement to do that, our accounts are managed on a cash-flow basis.
“But every penny we raise to support the campaign for independence will be spent on the campaign for independence.”
An SNP spokesman said: “We will co-operate fully with any investigation. As we have made clear, all sums raised for independence campaigning will be spent on independence campaigning.”
Responding to news of the police investigation, Scottish Conservative MSP Stephen Kerr said: “The SNP have failed to be fully transparent over this funding for months.
“Senior figures have resigned from the party’s Executive Committee over the matter but the SNP leadership have still not addressed these serious claims.
“The public to deserve to know the truth.
“It is only right that Police Scotland are stepping up their investigations, having received numerous complaints.”