Several dozen observations with the ROSAT PSPC are used to measure flu
ctuations of the unresolved X-ray background using the autocorrelation
function. At the lowest separation of 1 - 3 arc min a signal of (6.8
+/- 2.5) . 10(-3) has been detected. At larger separations (3 - 27 arc
min) the data are dominated by statistical noise. The average amplitud
e of the correlation function in the range of 3 - 11 arc min amounts t
o (0.3 +/- 0.9). 10(-3). The tight upper limit on the angular correlat
ion function severly constrains the clustering properties of sources p
roducing the background. In particular, it can be shown that contribut
ion of QSO to the residual background cannot exceed approximately 35 %
. Low luminosity AGN (probably Seyfert galaxies) are likely candidates
for the unresolved background. In this case they have to be weakly cl
ustered and show relatively strong clustering evolution.