We report on about 4 hrs of observations made with the Rossi X-ray Timing Explorer on 1997 May 2 of the low-mass X-ray binary and Z source GX 349+2 ( Sco X-2 ) . Initially the source was in the normal branch ( NB ) , later it moved to the flaring branch ( FB ) . In the NB the power spectra reveal a broad ( FWHM \sim 16 Hz ) noise component peaking near 9 Hz , with a fractional rms amplitude of \sim 3 % ( 2–30 keV ) . This noise component does not resemble the strong quasi-periodic oscillations ( QPO ) usually seen in the NB of other Z sources . We set 95 % confidence upper limits on the fractional rms of \sim 0.9 % ( 2–30 keV ) on any such QPO . In the FB the power spectrum showed a somewhat less broad noise component ( FWHM \sim 11 Hz ) peaking near 6 Hz with a fractional rms of \sim 4 % ( 2–30 keV ) . We compare our results with previous reports , and find that the fast timing behaviour changes not only with position in the Z , but also as a function of the position of the Z track in the hardness-intensity diagram . By comparing GX 349+2 with the other Z and atoll sources , we conclude that GX 349+2 differs from the Z sources in various aspects and shows similarities to the behaviour seen in the bright atoll sources , such as GX 13+1 and GX 3+1 . We also searched for kilo-Hertz QPO , similar to those present in other Z sources . We only found weak evidence ( 2.6 \sigma confidence ) for a QPO near 1020 Hz with FWHM \sim 40 Hz and fractional rms of \sim 1 % . We note that this frequency and fractional rms are consistent with those expected and observed in the lower NB/FB of the Z sources Sco X-1 , GX 17+2 and Cyg X-2 .