Brian Carroll, of the PCS said, "This is crucial to our sector as our employers and Scottish Ministers continue to impose the same 1% pay cap as the UK government.
"Our message to Mr Swinney, the Deputy First Minister is - break the public sector pay freeze!"
The rolling programme began with PCS members in Registers of Scotland taking their one day strike on 8 December, followed by the National Museums Scotland strike on Boxing Day (26 December), closing the museum to the public.
Brian added, "Unfortunately, for our members across the Scottish sector, the implementation of Scottish Government Policy is not over. We enter the New Year with a renewed commitment to fair pay and a readiness to continue with the rolling programme."
The union is also calling on its members to submit an e-action to John Swinney calling for fair pay.
Brian said, "Over 140 members have done this so far but Mr Swinney hasn’t yet responded. We need many more members to take this up if it is to have an effect. If you are a PCS member, please complete and send the e-petition to him. The more members that do, the more likely it is to have an effect.