Labour councillor Michael Beall and Lib Dem councillor Stuart Jarvis have stepped down with immediate effect.
The decisions of Michael Beall, who represented Southcourt ward, and Stuart Jarvis, who represented the Gatehouse ward were announced this afternoon.
A by-election could now be triggered in each ward by two local electors requesting that one be held.
Confirmation of dates for the by-elections will follow once requests from electors have been received.
The by-elections must be held within 35 days of the district council receiving formal notice.
Labour leader at AVDC Robin Stuchbury said that Mr Beall’s reasons for resigning were not linked to Stuart Jarvis, and that the councillor had cited personal and family reasons.
Mr Stuchbury also said he would be welcomed with open arms if he did decide to return.
He said: “I shall miss his support and local impetus.
“My hope is that once he has managed to resolve the situation that he needs to resolve he can re-enter politics.
“We would welcome him back with open arms.”