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We report on diffuse X-ray emission associated with the nearby solitarymillisecond pulsar PSR J2124-3358 detected with XMM-Newton and Chandra. Theemission extends from the pulsar to the northwest by ~0.5 arcmin. The spectrumof 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 particlesin 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 diffuseemission is detected down to a 3-sigma limiting flux of $4-7\times10^{-15}$ergs s$^{-1}$ cm$^{-2}$.Comment: Accepted by A&A lette

Searches for diffuse X-ray emission around millisecond pulsars: an X-ray nebula associated with PSR J2124-3358