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Compact steady sources of X-ray emission have been detected at the positionsof at least two soft gamma-ray repeaters (SGRs). These sources have beeninterpreted as synchrotron nebulae powered by the neutron star that is causingthe bursts. We explore a plerion model for the sources surrounding SGRs wherethe steady observed emission is powered by the SGR bursts rather than by thespin-down of a pulsar. In this case there is no limit on the neutron starmagnetic field. We find that the synchrotron lifetime of the particles injectedinto the plerion around SGR1806-20 is long enough to smear out nebular emissionfrom individual bursts. Transient nebular emission would therefore not bedetected following an SGR burst. The combined radio emission from multipleburst injections is expected to have a steeper spectrum than that of a typicalplerion.Comment: 5 pages, compressed, uuencoded postscript file. To appear in Proc. of  1995 La Jolla Workshop "High Velocity Neutron Stars and Gamma-Ray Bursts" ed.  R. Rothschild et al. (AIP: New York

The nature of plerions surrounding soft gamma-ray repeaters