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+-7 Hz to 296+-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%.
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