A security system is disclosed which is suitable for use in a passive entry and passive starting arrangement for a vehicle 10. A set of transmitters in the form of coils A, B, C are spaced around the vehicle 10, one A, B in each door mirror 20R, 20L and one in a high level brake light 16 at the rear end.Operation of a door handle initiates an access challenge from the vehicle 10 which is sent out successively on a plurality of the coils A, B, C. A portable transponder 26 carried by an authorised user is adapted to pick up the challenge signal and send back to a security controller 18 a response signal in which is included vector information relating to the relative positioning between the vehicle 10 and the transponder 26.