In recent observations with the Rossi X–Ray Timing Explorer we have detected two simultaneous quasi-periodic oscillation ( QPO ) peaks in the low mass X–ray binary and atoll source 4U 1735–44 . The lower and higher frequency QPOs have frequencies varying between 632 and 729 Hz , and 982 and 1026 Hz , respectively . The fractional rms amplitudes are 3.7 to 8.1 % and 5.0 to 5.8 % . The frequency separation between the two QPOs changes from 341 \pm 7 Hz to 296 \pm 12 Hz . The inferred mass accretion rate during our observations is relatively low compared to that during the previous observations , where only a single QPO was present . There is weak evidence that the frequency of the QPOs correlates with the mass accretion rate , as observed in other binaries . Five X–ray bursts were recorded with no detectable oscillations with upper limits for the rms fraction of 4 % to 13 % .