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 1x 10^−7 −5 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(ν) ν^-α ) to the 1 10^−7 −5 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 ( α<≈ 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 <≈ α <≈ 1.2) than type I sources. Type III systems are the most variable (rms > 30%) and exhibit the steepest power spectra ( α > 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 di erences in these systems may be caused by the presence of di erent 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 a ect their low-frequency X-ray aperiodic varibility.