Two Sinn Fein activists, one a prominent republican and the other a former IRA prisoner have received death threats.
Police informed the two men, neither of whom are elected, that their lives are at risk.
But both men say they will not leave their homes in Londonderry.
Party MLA Raymond McCartney said indications suggest that the threat has come from dissident republicans.
He added: “The first either of these men knew about this is when the police came to their doors and told them about that their lives were at risk.
“Indications from the PSNI would suggest that the dissidents are behind them but we cannot work out why.
“I spoke to both party members and neither will be deterred from doing the work they do on a day and daily basis for the people of Derry.
“It is difficult to make sense of the nonsensical, but both men are able to keep a real perspective.
“They are both family men and it is not nice having police coming to your door telling you there is a threat against you in the run up to Christmas.”
Dissident republicans have been at the forefront of threats against people living in Derry and to date are directly linked to 73 attacks and shootings in the Derry and Strabane areas and to the murder of Andy Allen in Co Donegal. Mr McCartney called on the people who made the threats to lift them.
He continued: “These threats should not be in place in the first instance but whichever corner they have come from I would call on them to lift them immediately.
“There is no rationale behind them and we will be contact with the PSNI to determined the exact level of threat against our two party workers.”
A spokesman for the PSNI said: “We do not discuss the security of any individual.
“However, if we receive information that a person's life may be at risk we will inform the relevant persons accordingly. We never ignore anything which may put an individual at risk.”