The discovery of source states in the X-ray emission of black-hole binaries and neutron-star low-mass X-ray binaries constituted a major step forward in the understanding of the physics of accretion onto compact objects. While there are numerous studies on the correlated timing and spectral variability of these systems, very little work has been done on high-mass X-ray binaries, the third major type of X-ray binaries. The main goal of this work is to investigate whether Be accreting X-ray pulsars display source states and characterise those states through their spectral and timing properties. We have made a systematic study of the power spectra, energy spectra and X-ray hardness-intensity diagrams of nine Be/X-ray pulsars. The evolution of the timing and spectral parameters were monitored through changes over two orders of magnitude in luminosity. We find that Be/X-ray pulsars trace two different branches in the hardness-intensity diagram: the horizontal branch corresponds to a low-intensity state of the source and it is characterised by fast colour and spectral changes and high X-ray variability. The diagonal branch is a high-intensity state that emerges when the X-ray luminosity exceeds a critical limit. The photon index anticorrelates with X-ray flux in the horizontal branch but correlates with it in the diagonal branch. The correlation between QPO frequency and X-ray flux reported in some pulsars is also observed if the peak frequency of the broad-band noise that accounts for the aperiodic variability is used. The two branches may reflect two different accretion modes, depending on whether the luminosity of the source is above or below a critical value. This critical luminosity is mainly determined by the magnetic field strength, hence it differs for different sources.
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