Nicola Sturgeon called for victims to come forward
It comes as party leader Nicola Sturgeon called for people to come forward with allegations of misconduct.
The First Minister had claimed she did not know of any allegations against SNP politicians but that she expected complaints in the wake of accusations in Westminster and the Harvey Weinstein scandal.
In a statement tonight, the party said both claims, brought by two separate people, would be fully investigated, but did not reveal further details.
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A spokesman for the SNP said: "The SNP has had concerns of this nature raised by two different individuals.
"The individuals and their concerns are unconnected to each other.
"These will be fully investigated but inquiries remain at an early stage.
"We will do nothing to deter people from coming forward and, as such, we will not comment further while investigations are ongoing."
It comes as a confidential phone-line was set up following "disturbing and deeply concerning" reports of sexual abuse or harassment in the Scottish Parliament.
Human rights lawyer Aamer Anwar said women ranging from MSPs to interns had made complaints and he accused politicians of maintaining an "abject silence" on the issue.
Earlier, Ms Sturgeon had proposed a cross-party review of parliamentary procedures and said Holyrood should be prepared to confront any allegations "head-on".
She said: "I fully expect that we will have concerns coming forward, like every political party will, and we will investigate them, if they come forward, in an appropriate way.
"I don't think any party can assume it's immune from behaviour like this, we want to think we are, but what I'm determined about is that if there are any issues raised associated with the SNP, they will be properly and rigorously investigated.”
It comes as allegations of impropriety sweep Westminster with reports of a list circulating containing the names of MPs suspected of misconduct.
Over the weekend the Prime Minister ordered a Cabinet Office inquiry into whether International Trade Minister Mark Garnier had breached the ministerial code over claims he asked his Commons secretary to buy sex toys.
Mrs May also faced calls to suspend former Cabinet minister Stephen Crabb, after he was reported to have admitted sending explicit messages to a 19-year-old woman he interviewed for a job.