It is known that the overall (mean) intensity of the low-mass X-ray binary
Cyg X-2 varies on time-scales from a day to months, independently of the va
riations on time-scales of hours to a day by which the source moves between
the horizontal, normal and flaring branches.
We present RXTE PCA observations of Cyg X-2, taken when its overall intensi
ty was near its lowest values, in 1996 October and 1997 September. For the
first time we perform a study of the fast timing behaviour at such low inte
nsities. During the 1996 October observations, the source was in the left p
art of the horizontal branch, and during the 1997 September observations wa
s most likely in the lower parts of the normal branch and flaring branch.
We find that the properties of the very low-frequency noise during the 1997
September observations are consistent with a monotonic decrease in its str
ength and power-law index as a function of overall intensity. In contrast,
the strength of the similar to 6 Hz normal branch quasiperiodic oscillation
s does not vary monotonically with overall intensity. They are strongest at
medium overall intensity and weaker both when the overall intensity is low
and when the overall intensity is high.