Employees at BBC Radio Lincolnshire and Look North will hold a 48 hour strike next month.
Members of the NUJ (National Union of Journalists) for BBC Local will take action across the country in response to cuts.
The new strikes dates have been announced for Wednesday, June 7 and Thursday, June 8.
It is part of an ongoing dispute over the BBC’s plans to cut local radio, which could mean only 40 hours of guaranteed weekly programming.
A statement by the NUJ this morning says: “The BBC wants to increase its digital output – but pay for it by cutting live, local radio on 39 stations – after 2pm and at the weekends.
“Industry leaders, MPs and former regulators have all questioned the impact on Local Radio’s 5.7million listeners.
“We’re also deeply concerned about other changes that could adversely affect output both on TV and online.
“NUJ members across BBC Local will take part in the 48 hour strike.”
Previous strikes took place in March and over the local elections earlier this month.
Earlier this week, veteran Radio Lincolnshire presenter Melvyn Prior announced he would be leaving the station later this year.
“Change is always difficult, but this process has been painful and has taken its toll on both those staying and those leaving,” he said.
Many radio presenters have been required to reapply for their jobs in a process which has been criticised as being similar to “the Hunger Games”.
Several big names at Radio Humberside have also announced their departures.
The BBC has previously said it would continue to engage with staff and do everything possible to minimise disruption on programming.
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