  We report on diffuse X-ray emission associated with the nearby solitary
millisecond pulsar PSR J2124-3358 detected with XMM-Newton and Chandra. The
emission extends from the pulsar to the northwest by ~0.5 arcmin. The spectrum
of the nebular emission can be modeled with a power-law of photon index
$2.2\pm0.4$, in line with the emission originating from accelerated particles
in the post shock flow. For PSR J0437-4715, PSR J0030+0451 and PSR J1024-0719,
which all have spin parameters comparable to that of PSR J2124-3358, no diffuse
emission is detected down to a 3-sigma limiting flux of $4-7\times10^{-15}$
ergs s$^{-1}$ cm$^{-2}$.
