We analyzed a deep XMM-Newton observation of the radio-quiet γ-ray PSR J2055+2539. The spectrum of the X-ray counterpart is nonthermal, with a photon index of Γ=2.36±0.14 (1σ confidence). We detected X-ray pulsations with a pulsed fraction of 25% ± 3% and a sinusoidal shape. Taking into account considerations on the γ-ray efficiency of the pulsar and on its X-ray spectrum, we can infer a pulsar distance ranging from 450 to 750 pc. We found two different nebular features associated withPSR J2055+2539 and protruding from it. The angle between the two nebular main axes is ∼162°.8±0°.7. The main, brighter feature is 12′ long and <20″ thick, characterized by an asymmetry with respect to the main axis that evolves with the distance from the pulsar, possibly forming a helical pattern. The secondary feature is 250″×30″. Both nebulae present an almost flat brightness profile with a sudden decrease at the end. The nebulae can be fitted byeithera power-law model or a thermal bremsstrahlung model. A plausible interpretation of the brighter nebula is in terms of a collimated ballistic jet. The secondary nebula is most likely a classical synchrotron-emitting tail.