Alastair Majury and Robert Davies are being investigated by the Scottish Conservatives over their comments.
Police Scotland has also received a report of comments made on social media by Mr Davies.
Mr Majury and Mr Davies were recently elected to the wards of Dunblane and Bridge of Allan, and Forth and Endrick.
Councillor Davies has been accused of sending racist posts from a Twitter account in 2013 which was subsequently deleted.
The Scottish Catholic Observer reported that a Twitter account previously used by Mr Majury under the name Mulder1981 made reference to 'Tarriers', a historically derogatory name for Catholics.
A Scottish Conservatives spokesman said: "Both councillors have been suspended from the party pending an investigation."
A Police Scotland spokeswoman said: "Police in Forth Valley can confirm that a report of offensive communications on social media was received on Wednesday May 10 and inquires are ongoing."
Two newly-elected Conservative councillors in Stirling have been suspended by the party over offensive posts made on Twitter.