We present the results of a series of XMM-Newton EPIC and OM observations of
Her X-1, spread over a wide range of the 35 d precession period. We confirm
that the spin modulation of the neutron star is weak or absent in the low state
- in marked contrast to the main or short-on states. The strong fluorescence
emission line at ~6.4 keV is detected in all observations (apart from one taken
in the middle of eclipse), with higher line energy, width and normalisation
during the main-on state. In addition, we report the detection of a second line
near 7 keV in 10 of the 15 observations taken during the low-intensity states
of the system. We discuss these observations in the context of previous
observations, investigate the origin of the soft and hard X-rays and consider
the emission site of the 6.4keV and 7keV emission lines.