Vacancies have occurred on Gosberton and Sutton Bridge parish councils.
At Sutton Bridge the vacancy has arisen due to the resignation of Gary Croxford.
For elections to be held, ten people must request one by March 28, otherwise the vacancies will be filled by co-option.
Any request must be made in writing to: Vicky Thomson, Returning Officer, Council Offices, Priory Road, Spalding PE11 2XE.
If elections are called, they will take place before June 5.