The town council is advertising seats in St Clements ward following the resignation of Carole Lambert, and Elms ward after Rosemary Arscott, the mother of current chairman Bernard Arscott stepped down.
Mrs Arscott is said to be suffering from ill health while Ms Lambert is believed to have found work pressures impacting council duties.
Mr Arscott, town councillor for Highlands ward, said: “Rosemary has decided to stand down because she’s realised with her health not being quite where she wants it to be. She’s decided to step down.
“Carole has had a career change that makes it very difficult for her to be involved in council business at present so she’s decided to stand down to develop her career and we wish her the best for that.”
Paul Gilson, Conservative town councillor for Thames Ward, said: “It’s a shame they are both going. Rosemary is an intelligent lady but her health has just not improved.
“You’ve got to have spare time to do the job properly. There is a lot to do, a huge amount of meetings and organising new staff but it’s an exciting time for the council and we welcome applications for the vacancies.”
Last year the council saw the resignation of three town councillors amid a period of turmoil for he council. Police were called to a meeting which turned rowdy after residents called councillors to account over claims of a lack of transparency.
There were also protests after the council instigated an audit of council staff which saw a new town clerk appointed.
Vice chairman Carole Mulroney is currently the only town councillor in St Clement’s Ward.
She said: “Both the resignations happened just before Christmas.
“The election for St Clement’s ward has already been called and I’m going to call one for Elms ward. I don’t think they will be quick because it’s all organised by the city and we’ve got the budget coming up so it’s a busy time.”