We report on the analysis of archival ASCA, ROSAT and BeppoSAX data of PSR B1055−52, PSR B0656+14 and Geminga, performed in order to investigate the reality of the putative ∼ 10–20 arcmin wide X-ray pulsar-wind nebulae recently proposed to exist around these pulsars. In all these cases, the ROSAT and/or BeppoSAX data show that the diffuse and clumpy X-ray nebulae found by ASCA can be resolved i...