We present an analysis of 30 archival ASCA and RXTE X-ray observations of 16 intermediate polars to investigate the nature of their orbital modulation. We show that X-ray orbital modulation is widespread amongst these systems, but not ubiquitous as indicated by previous studies that included fewer objects. Only seven of the sixteen systems show a clearly statistically significant modulation depth whose amplitude decreases with increasing X-ray energy. Interpreting this as due to photoelectric absorption in material at the edge of an accretion disc would imply that such modulations are visible for all system inclination angles in excess of 60 degrees. However, it is also apparent that the presence of an X-ray orbital modulation can appear and disappear on a timescale of ~years or months in an individual system. This may be evidence for the presence of a precessing, tilted accretion disc, as inferred in some low mass X-ray binaries.
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