  The eclipsing brown-dwarf binary system 2MASS J05352184-0546085 is a case sui
generis. For the first time, it allows a detailed analysis of the individual
properties of young brown dwarfs, in particular, masses, and radii, and the
temperature ratio of the system components can be determined accurately. The
system shows a "temperature reversal" with the more massive component being the
cooler one, and both components are found to be active. We analyze X-ray images
obtained by Chandra and XMM-Newton containing 2MASS J05352184-0546085 in their
respective field of view. The Chandra observatory data show a clear X-ray
source at the position of 2MASS J05352184-0546085, whereas the XMM-Newton data
suffer from contamination from other nearby sources, but are consistent with
the Chandra detection. No indications of flaring activity are found in either
of the observations (together about 70 ks), and we thus attribute the observed
flux to quiescent emission. With an X-ray luminosity of 3*10^{28} erg/s we find
an L_X/L_{bol}-ratio close to the saturation limit of 10^{-3} and an
L_{X}/L_{H\alpha}-ratio consistent with values obtained from low-mass stars.
The X-ray detection of 2MASS J05352184-0546085 reported here provides
additional support for the interpretation of the temperature reversal in terms
of magnetically suppressed convection, and suggests that the activity phenomena
of young brown dwarfs resemble those of their more massive counterparts.
