A statement by new councillors Marc Jones (Grosvenor), Gwenfair Jones (Gwersyllt West) and Carrie Harper (Queensway) said:
"We're very proud to be elected to serve our communities and grateful for the support Plaid Cymru has received across the borough.
"Our task now is to implement as much of our manifesto as we can and work with everybody who wants to change Wrexham for the better.
"People have felt in the past that the council doesn't listen, isn't responsive and is happy to do deals behind closed doors. That's got to change if the council is to win back confidence from the people who elect them.
"One specific problem we have is that Wrexham now has two groups of independents who effectively act as political parties but don't declare that in their leaflets. They divvy up jobs on the council behind closed doors and will be deciding on who will get the top jobs. How many people voted for independents believing that was the way forward?
"Independents should not be able to act as secret parties unless they're willing to sign up to an agreed set of policies in advance. With a few honourable exceptions, the so-called independent councillors are already in the pockets of one of the two independent groups that operate on the council.
"We want to shine a spotlight on how the council is run. We want greater democracy and for residents to have a greater say.
"During the election campaign, we distributed thousands of copies of our detailed manifesto to voters. It's online at www.plaidwrecsam.cymru and we'll be using that as a plan of action over the coming weeks and months to highlight ways to involve the people in decision making."