  Important constraints on the properties of the Anomalous X-ray Pulsars (AXPs)
and Soft Gamma-Ray Repeaters (SGRs) can be provided by their associations with
supernova remnants (SNRs). We have made a radio search for SNRs towards the
AXPs RX J170849-400910 and 4U 0142+61 - we find that the former lies near a
possible new SNR with which it is unlikely to be physically associated, but see
no SNR in the vicinity of the latter. We review all claimed pairings between
AXPs and SNRs; the three convincing associations imply that AXPs are young (<
10 000 yr) neutron stars with low projected space velocities (< 500 km/s).
Contrary to previous claims, we find no evidence that the density of the
ambient medium around AXPs is higher than that in the vicinity of radio
pulsars. Furthermore, the non-detection of radio emission from AXPs does not
imply that these sources are radio-silent. We also review claimed associations
between SGRs and SNRs. We find none of these associations to be convincing,
consistent with a scenario in which SGRs and AXPs are both populations of
high-field neutron stars ("magnetars") but in which the SGRs are an older or
longer-lived group of objects than are the AXPs. If the SGR/SNR associations
are shown to be valid, then SGRs must be high-velocity objects and most likely
represent a different class of source to the AXPs.

Astrophysics