The result of the strike ballot is due on 9 December.
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More than 7,000 workers in magistrates' courts are being sent strike ballot papers after pay talks broke down.
The Public and Commercial Services and Prospect unions said the cost-of-living part of the offer equalled a below- inflation rise of 2.2% for most staff.
They warned a planned 24-hour strike next month would close some courts in England and Wales and disrupt others.
But the Department for Constitutional Affairs said the deal was worth a total of 3.7% and negotiations were ongoing.
In a statement, it said robust contingency plans had been put in place to enable essential services, including the courts, to remain open.
'Intolerable situation'
The Public and Commercial Services (PCS) union said that 51% of court staff earned less than £15,000 a year.
PCS national secretary Rosie Eagleson said: "Balloting for strike action is not a step we take lightly but members are growing increasingly angry with an attempt by management to further devalue their pay..."
General secretary Mark Serwotka added: "The intolerable situation with magistrate staff's pay underlines the mess that civil service pay is in...
"Members are right to be angry and will vote for industrial action to secure justice on their pay."
The unions said the pay dispute followed the establishment in April of the combined courts agency, Her Majesty's Court Service (HMCS).
They said the Department for Constitutional Affairs had failed to properly fund the start-up costs of HMCS.
Prospect national secretary Alan Leighton said: "It is disgraceful that staff are expected to pay the price for the creation of HMCS.
"They are not prepared to accept a real terms pay cut as a welcome present for joining the civil service."
The result of the strike ballot is due on 9 December.