  We report on the X-ray spectral variability of the Seyfert 1 galaxy NGC 4051
observed with the Rossi X-ray Timing Explorer (RXTE) during a 1000 day period
between May 1996 and March 1999. The spectra were obtained as part of
monitoring observations and from two long observations using the RXTE
Proportional Counter Array (PCA). During the monitoring period the 2-10 keV
flux of NGC 4051 varied between 10E-12 and 7x 10E11 (cgs). We re-analysed RXTE
PCA observations from a distinct low state in May 1998 using the latest
background and detector response models. The RXTE and BeppoSAX observations of
NGC 4051 during the low state show a very hard spectrum with a strong
unresolved fluorescence line. This emission, probably due to reflection from a
molecular torus, is likely to be constant over long time-scales and is
therefore assumed as an underlying component at all flux states. By subtracting
the torus component we are able to determine the spectral variability of the
primary continuum. In the variable component we observe a strong
anti-correlation of X-ray flux and spectral hardness in the PCA energy band. We
show that the changes in hardness are caused by slope variability of the
primary power law spectrum rather than by changing reflection or variable
photoelectric absorption. The primary spectral index varies between Gamma=1.6
for the faintest states and Gamma=2.3 during the brightest states, at which
level the spectral index approaches an asympotic value. We find that the
response of the flux of the 6.4 keV iron fluorescence line to changes in the
continuum flux depends on the timescale of the observation. The profile of the
line is very broad and indicates an origin in the innermost regions of the
accretion disk.
