Pointed ROSAT PSPC exposures of 9277 and 6992 sec, directed toward the nearby, single, cool, magnetic white dwarfs GR 290 and EG 250 yielded no counts significantly above the expected background rate. The corresponding flux limits (for an assumed source temperature of l keV) are 1.0 and 1.7 × 10-14erg cm-2 s-1, within the 0.1-2.5 keV bandpass of the instrument (99% confidence limits). This is more than an order of magnitude below the tentative detection level (for GR 290) and limits (for four other similar stars) obtained from archival Einstein data in 1991. The corresponding limits on coronal electron density are comparable with those implied if cyclotron emission is not responsible for any of the features observed in the optical spectra of magnetic white dwarfs. X-ray data currently provide no evidence for the existence of coronae around these stars. A final long observation (25,000 sec of GD 356) is scheduled for later this year on ROSAT, along with coordinated EUVE observations. © 1993 Indian Academy of Sciences.