We have analyzed 17 observations of the low-mass X-ray binary and atoll sou
rce 4U 1728-34, carried out by the Rossi X-Ray Timing Explorer in 1996 and
1997. We obtain precise measurements of the frequencies of the two simultan
eous kilohertz quasi-periodic oscillations (kHz QPOs) in this source. We sh
ow that the frequency separation between the two QPO, Delta nu, is always s
ignificantly smaller than the frequency of the nearly coherent oscillations
seen in this source during X-ray bursts, even at the lowest inferred mass
accretion rate, when Delta nu seems to reach its maximum value. We also fin
d that Delta nu decreases significantly, from 349.3 +/- 1.7 Hz to 278.7 +/-
11.6 Hz, as the frequency of the lower frequency kHz QPO increases from 61
5 to 895 Hz. This is the first time that variations of the kHz QPO peak sep
aration are measured in a source that shows nearly coherent oscillations du
ring bursts.