Analysis of data from the Rossi X-ray Timing Explorer satellite's All Sky Monitor (ASM) instrument for several X-ray binary sources has identified a recurrent ∼24 h period. This period is sometimes highly significant, giving rise to the possibility of it being identified as an orbital or super-orbital period. Further analysis has revealed the same period in a number of other X-ray sources. As a result this period has been discounted as spurious, described variously as arising from daily variations in background levels, the scheduling of ASM observations and beating between the sampling period and long-term secular trends in the light curves. We present here an analysis of the spurious periods and show that the dominant mechanism is in fact spectral leakage of low-frequency power present in the light curves.