Residents in south Essex are being asked to decide if they want a council leader or a mayor.
People in Thurrock must decide who will preside over a governing cabinet so arrangements are in place by May 2011.
Both options would see the election of an individual who would then appoint a cabinet of up to nine councillors.
The leader and cabinet option is similar to the council's current structure. Both council arrangements would run for a four-year term.
The council would not be able to remove a directly-elected mayor from office.
Under this system, the title of civic mayor, as Thurrock has at present, would disappear.
The council would be able to remove the leader from office and a civic mayor would continue to be appointed annually to carry out ceremonial and other duties.
Thurrock Council has launched a short, six-week online consultation which will feedback the public's initial thoughts and opinions to the council and cabinet.
A more detailed consultation will be held later in the year.