We have observed M31 using the ROSAT HRI. We have searched for X-ray e
mission from supernova remnants (SNRs) previously identified from surv
eys using narrowband optical observations. We find that a surprisingly
small number of the identified SNRs are detected in X-rays at a thres
hold of approximate to 10(35) ergs s(-1). The absence of detected X-ra
y flux from many of the optically identified SNRs suggests that the lo
cal ISM density in the vicinity of these SNRs is typically quite low,
less than 0.1 cm(-3). The few that have been detected likely represent
the upper end of the density distribution, having implied ambient den
sities in the range 0.1 to >10 cm(-3). Since H I observations show tha
t all SNRs are in regions with large column densities, which implies d
ensities of 1-10 cm(-3), a multicomponent ISM must be invoked. Our mea
sured densities are upper limits for the dominant low-density componen
t of the ISM.