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 .