The Rossi X-Ray Timing Explorer observed the soft X-Ray transient Aql X-1 during its outburst in February and March 1997 . We report the discovery of quasi-periodic oscillations ( QPOs ) in its persistent flux with frequencies in the range of 740 to 830 Hz , Q-value of over 100 , and a fractional RMS amplitude of ( 6.8 \pm 0.6 ) % , and nearly coherent oscillations ( NCOs ) during a Type-I burst with a frequency of 549 Hz . The frequency of the QPOs in the persistent flux is correlated with the mass accretion rate on time scale of hours , but not on time scale of days . This is most likely the manifestation in a single source of the kHz QPO puzzle observed among many sources , i.e. , on the one hand , individual sources show a correlation between the QPO frequency and the inferred mass accretion rate , on the other hand , the dozen or so sources with luminosities spanning two decades have essentially the same QPO frequencies . We propose that this multi-valued QPO frequency and mass accretion rate correlation indicates the existence of many similar regimes of the accretion disk . These regimes , with a very similar energy spectrum and QPO frequency , are distinguished from each other by the mass accretion rate or the total X-ray flux . The NCOs during the burst can be made almost perfectly coherent by taking into account a large \dot { \nu } . This strongly suggests that this frequency is related to the neutron star spin frequency . The large \dot { \nu } is attributable to the expansion or contraction of the neutron star photosphere during the burst .