  We have carried out a systematic study of the properties of the kilo-Hertz
quasi-periodic oscillations (QPO) observed in the X-ray emission of the neutron
star low-mass X-ray binary 4U1608-52, using archival data obtained with the
Rossi X-ray Timing Explorer. We have investigated the quality factor, Q, of the
oscillations (defined as the ratio of the frequency of the QPO peak to its full
width at half maximum). In order to minimise the effect of long-term frequency
drifts, power spectra were computed over the shortest times permitted by the
data statistics. We show that the high Q of ~200 reported by Berger et al.
(1996) for the lower frequency kilo-Hz QPO in one of their observations is by
no means exceptional, as we observe a mean Q value in excess of 150 in 14 out
of the 21 observations analysed and Q can remain above 200 for thousands of
seconds. The frequency of the QPO varies over the wide range 560--890 Hz and we
find a systematic trend for the coherence time of the QPO, estimated as tau=Q
/(pi nu), to increase with the frequency, up to a maximum level at ~ 800 Hz,
beyond which it appears to decrease, at frequencies where the QPO weakens.
There is a more complex relationship between tau and the QPO root mean squared
amplitude (RMS), in which positive and negative correlations can be found. A
higher-frequency QPO, revealed by correcting for the frequency drift of the
560-890 Hz one, has a much lower Q (~10) which does not follow the same
pattern. We discuss these results in the framework of competing QPO models and
show that those involving clumps orbiting within or above the accretion disk
are ruled out.
