  We report on the analysis of new X-ray data obtained with XMM-Newton and
Chandra from two ROSAT-discovered X-ray dim isolated neutron stars. RX
J0806.4-4123 was observed with XMM-Newton in April 2003, 2.5 years after the
first observation. The EPIC-pn data confirm that this object is an X-ray pulsar
with 11.371 s neutron star spin period. The X-ray spectrum is consistent with
absorbed black-body emission with a temperature kT = 96 eV and NH = 4x10^19
cm^-2 without significant changes between the two observations. Four XMM-Newton
observations of RX J0420.0-5022 between December 2002 and July 2003 did not
confirm the 22.7 s pulsations originally indicated in ROSAT data, but clearly
reveal a 3.453 s period. A fit to the X-ray spectrum using an absorbed
black-body model yields kT = 45 eV, the lowest value found from the small group
of XDINs and NH = 1.0x10^20 cm^-2. Including a broad absorption line improves
the quality of the spectral fits considerably for both objects and may indicate
the presence of absorption features similar to those reported from RBS1223, RX
J1605.3+3249 and RX J0720.4-3125. For both targets we derive accurate X-ray
positions from the Chandra data and present an optical counterpart candidate
for RX J0420.0-5022 with B = 26.6+/-0.3 mag from VLT imaging.
