Members of the Public and Commercial Services Union (PCS) at the National Museum of Scotland have voted in support of strike action in a row over weekend allowance payments.
And PCS members at the National Galleries of Scotland, also in Edinburgh, could also be balloted for strike action over the potential withdrawal of weekend allowances.
For several years, new staff at the museum have not been paid enhanced payments for weekend working, which are paid to staff who have been there longer than three years.
In a vote, strike action was supported by 96% of members taking part and the museum branch of the union will meet this morning to decide on possible strike action.
PCS members at the National Museum joined their colleagues at the National Galleries of Scotland who were protesting at the annual Patrons' Dinner last week.
Management at the National Galleries also wish to withdraw the weekend allowance paid to visitor service and retail staff.
Lynn Henderson, Scottish secretary of the PCS, said: "Yet again low-paid workers are asked to bear the burden of budget cuts in the Scottish culture sector."
"But this time they have had enough and voted overwhelmingly to take industrial action to protect their pay from morally indefensible attacks."
The union would have to inform the NMS of any strike action seven days before making any such move.
A spokesman for National Museums Scotland said: "Like many other public sector organisations, National Museums Scotland has had to make a wide range of changes in order to manage the reduced budgets which have been a result of the financial crisis.
"These changes have included reducing staff numbers, reducing a range of budgets, constraining some services and introducing a change to some terms and conditions for staff newly appointed to ensure that we could continue to operate within the funding available."
He added: "The changes to weekend premia came into force three years ago in January 2011 for new staff.
"We have maintained these payments for staff employed prior to 2011 and as staff retire and move on these will be phased out."
He added that only around half of the museum staff who work weekends receive a premium payment and such payments are no longer common within organisations in the sector.
The PCS has 95 members at the NMS and 80 at the National Galleries.
A statement from the NGS said negotiations between the galleries and trade union are ongoing about a pay offer which includes the removal of a weekend working allowance.
"At present some staff receive an additional allowance for working on Saturdays and Sundays," a spokeswoman said.
"However, in line with current practice across the cultural and heritage sector in the UK, we have proposed to discontinue this allowance from next year."