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 \sim 0.5 arcmin .
The spectrum of the nebular emission can be modeled with a power-law of photon index 2.2 \pm 0.4 , 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 \sim 4 - 7 \times 10 ^ { -15 } ergs s ^ { -1 } cm ^ { -2 } .