We report the detection of luminous extended X-ray emission in NGC 624
0 on the basis of ROSAT HRI observations of this ultraluminous IR gala
xy. The spatial structure and temporal behavior of the X-ray source we
re analyzed. We find that greater than or similar to 70% of the soft X
-ray emission is extended beyond a radius of 5 ''. Strong emission can
be traced out to a radius of 20 '' and weaker emission extends out to
similar to 50 ''. With a luminosity of at least L-x similar or equal
to 10(42) erg/s this makes NGC 6240 one of the most luminous X-ray emi
tters in extended emission known. Evidence for a nuclear compact varia
ble component is indicated by a drop of 32% in the HRI count rate as c
ompared to the PSPC data taken one year earlier. No short-timescale va
riability is detected. The HRI data, which represent the first high-re
solution study of the X-ray emission from NGC 6240, complement previou
s spectral fits to ROSAT PSPC data that suggested a two-component mode
l consisting of thermal emission from shocked gas immersed in a starbu
rst wind plus a powerlaw source attributed to scattered light from an
obscured AGN. We discuss several models to account for the extended an
d compact emission. Although pushed to its limits the starburst outflo
w model is tenable for the essential part of the extended emission. Fo
r the AGN-type component we propose a model consisting of a near-nucle
ar 'warm scatterer' that explains the apparent fading of the X-ray flu
x within a year as well as the strong FeK alpha complex seen in an ASC
A spectrum.