************************************************************************* 52084 Common wisdom tells us that there must exist some relativistic outflow from the Vela pulsar which would explain its rotational energy loss rate. Recent ROSAT and ASCA observations of a jet-like structure near the Vela pulsar suggest that the pulsar is driving a jet into its supernova remnant. We found a partially thermal spectrum at the head of the jet, but the ASCA spectrum of the jet "body" is unknown. If the body is purely thermal, then we interpret the jet as a hot plasma "cocoon" surrounding the jet itself. If instead the body spectrum is purely non-thermal, then it would be similar to another pulsar jet of PSR 1509-58, recently discovered by ASCA. *************************************************************************