I discuss morphology and spectrum of the first resolved and detected classical nova shell in the X-rays - the remnant of GK Persei (1901). The existence of such a nebulosity brings about the possibility of other nova remnants emitting X-rays. I calculate that the X-ray luminosity should be about 10(26) - 10(33) ergs s(-1) on the onset of cooling for nova remnants. I have done an archival search on 250 classical and recurrent nova candidates using Chandra, XMM-Newton, ROSAT and ASCA databases. There is no significant extended emission detected which places an upper limit of F(x) < x 10(-12) erg s(-1) cm(-2) (unabsorbed). Only exceptions are GK Per, RR Pic and DQ Her (all observed by Chandra ACIS-S and GK Per also by ROSAT HRI) where the latter two show marginal extended emission in the X-rays associated with emission knots (DQ Her) or an equatorial ring (RR Pic). (c) 2006 Published by Elsevier Ltd on behalf of COSPAR.