The NUJ vote was 61% in favour of stoppages, while backing among Bectu members was 56%.
Paul McManus, from the Broadcasting Entertainment Cinematograph and Theatre Union (Bectu), also appeared before the committee.
Broadcasting union Bectu and the National Union of Journalists will ballot members in the coming weeks.
Last Thursday, members of the National Union of Journalists and Bectu staged a 12-hour strike, affecting programmes including news bulletins.
"BBC staff have today rejected management's attempts to create a modern-day BBC sweatshop, " said Bectu leader Gerry Morrissey.
Members of the National Union of Journalists (NUJ) and technical union Bectu voted in favour of the walkouts.
David Donovan, national officer for Bectu, said the strike sent a "clear message".
Members of the National Union of Journalists and Bectu, representing technical staff, voted in favour of the walkouts earlier this month.
Bectu told the BBC News website that 39% of the 3, 800 BBC Bectu members affected by DQF had voted in the ballot.
Members of the Nationals Union of Journalists(NUJ) and Bectu union walked out at midday on Thursday, ahead of the Easter bank holiday.
Both unions were also in favour of action short of a strike, with 80% of NUJ members and 81% of Bectu's supporting it.
The dispute led to a 12-hour strike before Easter by members of the National Union of Journalists and Bectu, affecting programmes including news bulletins.
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Paul McManus, from the Broadcasting Entertainment Cinematograph and Theatre Union (BECTU), said reducing staff levels but increasing output and maintaining quality was "just not possible".
"The bill is a sensible and much needed response to what has become an unacceptable situation for those whose livelihoods depend on the success of the creative industries, " said Martin Spence, assistant general secretary of Bectu and a representative of CCC.
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