Gwynedd councillor Penri Jones resigned his position as the education portfolio leader, while another seniorcouncillor resigned from the Plaid Cymru group.
His comments come in the same week a seniorcouncillor from Cornwall's cabinet resigned over an alleged plan to use what she has described as "lie detector" technology.
Councillor Derek Davies said a senior planning barrister had advised the authority that there is a "strong case" to challenge the secretary of state's decision.