  We have obtained discrete Fourier power spectra of a sample of persistent
low-mass neutron-star X-ray binaries using long-term light curves from the All
Sky Monitor on board the Rossi X-ray Timing Explorer. Our aim is to investigate
their aperiodic variability at frequencies in the range 1 x 10^{-7}-5 x 10^{-6}
Hz and compare their properties with those of the black-hole source Cyg X-1. We
find that the classification scheme that divides LMXBs into Z and atoll sources
blurs at very low frequencies. Based on the long-term (~ years) pattern of
variability and the results of power-law fits (P ~ v^{-a}) to the 1 x 10^{-7}-5
x 10^{-6} Hz power density spectra, low-mass neutron-star binaries fall into
three categories. Type I includes all Z sources, except Cyg X-2, and the atoll
sources GX9+1 and GX13+1. They show relatively flat power spectra (a < 0.9) and
low variability (rms < 20%). Type II systems comprise 4U 1636-53, 4U 1735-44
and GX3+1. They are more variable (20% < rms < 30%) and display steeper power
spectra (0.9 < a < 1.2) than Type I sources. Type III systems are the most
variable (rms > 30%) and exhibit the steepest power spectra (a > 1.2). The
sources 4U 1705-44, GX354-0 and 4U 1820-30 belong to this group. GX9+9 and Cyg
X-2 appear as intermediate systems in between Type I and II and Type II and III
sources, respectively. We speculate that the differences in these systems may
be caused by the presence of different types of mass-donor companions. Other
factors, like the size of the accretion disc and/or the presence of weak
magnetic fields, are also expected to affect their low-frequency X-ray
aperiodic varibility.
