  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 from the
variations 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 intensity
was near its lowest values, in October 1996 and September 1997. For the first
time we perform a study of the fast timing behaviour at such low intensities.
During the October 1996 observations the source was in the left part of the
horizontal branch, and during the September 1997 observations 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
September 1997 observations are consistent with a monotonic decrease in its
strength and power-law index as a function of overall intensity. In contrast,
the strength of the ~6 Hz normal branch quasi-periodic oscillations do 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.
