A detailed derivation of the semiclassical form for the relativistic p
article propagator in arbitrary external electromagnetic held is prese
nted. To this end a path-integral representation is used. The final fo
rmula is a generalization of the Van Vleck-Pauli-Morette semiclassical
representation in the nonrelativistic quantum mechanics. We demonstra
te the efficiency of the former in the case of an arbitrary constant e
lectromagnetic field.