Two very promising candidates for isolated old neutron stars (IONS) ac
creting interstellar matter were found so far in ROSAT data. RXJ1856.5
-3754 and RXJ0720.4-3125 are soft X-ray sources with very similar X-ra
y spectrum, long term temporal behaviour and faint optical counterpart
. In addition RXJ0720.4-3125 shows 8.4 s pulsations which allow to con
strain the magnetic field strength of the neutron star. We carried out
a search for additional IONS with similar properties in the ROSAT all
-sky survey data of the galactic plane and present RXJ0806.4-4123 as f
urther promising candidate.