1. A periphery monitoring device for a vehicle comprising: object position detecting means for detecting positions of an object on the periphery of a vehicle at prescribed time intervals; expected object locus computing means for computing an expected locus of the object on the basis of the positions of the object detected by said object position detecting means; expected vehicle locus computing means for computing an expected locus of the vehicle; and danger determining means for determining whether or not there is a danger of collision between the object and the vehicle on the basis of both the expected loci of the object and the vehicle.