The positions on the committee will help scrutinise the work of the new elected Police Commissioner.
The two independent members will join 10 councillors, from both Wiltshire and Swindon coucils, on the new panel which will scruitinise the work of the commissioner.
The panel are looking for committed individuals who care about their communities. Members could be community representatives, have relevant knowledge and skills or be experts in their field.
The positions are unpaid, but reasonable travel expenses will be reimbursed. Members are expected to attend between 4 and 6 meetings each year in addition to around 1 day per month in preparation.
Anyone wanting to apply has to be over 18, not be an MP or MEP, a police officer or civil servant.