  We report for the first time on the rapid X-ray variability of the galactic
bulge source and X-ray burster SLX 1735-269. The power spectrum as observed
with the Rossi X-ray Timing Explorer is characterized by a strong band-limited
noise component which is approximately flat below a 0.1-2.3 Hz break frequency;
above this frequency the power spectrum declines as a power law of index 0.9.
At the highest observed count rate a broad bump is superimposed on this
band-limited noise. The power spectrum is very similar to that of other
low-luminosity neutron-star low-mass X-ray binaries (LMXBs) and to black-hole
candidates when these types of source accrete at their lowest observed mass
accretion rates. However, we identify one unusual aspect of the X-ray
variability of SLX 1735-269: the break frequency increases when the inferred
mass accretion rate decreases. This is the opposite to what is normally
observed in other sources. The only source for which the same behavior has been
observed is the accretion-powered millisecond X-ray pulsar SAX J1808.4-3658. No
coherent millisecond pulsations were observed from SLX 1735-269 with an upper
limit on the amplitude of 2.2% rms. Observing this behavior in SLX 1735-269
increases the similarities between SAX J1808.4-3658 and the other neutron star
LMXBs for which so far no coherent pulsations have been observed. We expect
that other sources will show the same behavior when these sources are studied
in detail at their lowest mass accretion rates.
