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 (XDINs). RX J0806.4−4123 was observed with XMM-Newton in April 2003, 2.5 years after\ud 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 N H = 4 × 10 19 cm −2 without significant changes between the two observations. Four XMM-Newton observations of RX\ud 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 N H = 1.0 × 10 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.\u
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