We report the results of ASCA and Ryle Telescope observations of the d
istant cluster of galaxies A1204. The X-ray image shows that this sour
ce is very compact and that the intracluster gas is strongly centrally
concentrated. The brightness temperature decrement of the cosmic micr
owave background radiation toward this cluster (the Sunyaev-Zeldovich
effect) was not detected by the Ryle Telescope, with a 1 sigma upper l
imit of \Delta T\ < 360 mu K. The gas temperature is 3.6 keV, which is
considerably lower than that expected from the bright X-ray luminosit
y in the ROSAT band and explains the lack of detection. The hot gas ma
ss within 1 Mpc is estimated to be less than or similar to 7 x 10(13)
M(.). In the wide window of the ASCA Gas Imaging Spectrometer, a very
faint X-ray source was found at R.A. = 11(h)12(m)16(s), decl. = +17 de
grees 56'40'' (J2000). The observed count rate was too small to identi
fy the X-ray emission mechanism in the new source.