We report the detection of changes in the long-term intensity variations in
two X-ray binaries, Cyg X-2 and LMC X-3. In this work, we have used the lo
ng-term light curves obtained with the All-Sky Monitors (ASMs) of the Rossi
X-Ray, Timing Explorer (RXTE), Ginga, Ariel 5, and Vela 5B and the scannin
g modulation collimator of HEAO 1. It is found that in the light curves of
both the sources, obtained with these instruments at various times over the
last 30 years, more than one periodic or quasiperiodic component is always
present. The multiple prominent peaks in the periodograms have frequencies
unrelated to each other. In Cyg X-2, RXTE-ASM data show strong peaks at 40
.4 and 68.8 days, and Ginga-ASM data show strong peaks at 53.7 and 61.3 day
s. Multiple peaks are also observed in LMC X-3. The various strong peaks in
the periodograms of LMC X-3 appear at 104, 169, and 216 days (observed wit
h RXTE-ASM) and 105, 214, and 328 days (observed with Gingn-ASM). The prese
nt results, when compared with the earlier observations of periodicities in
these two systems, demonstrate the absence of any stable long period. The
78 day periodicity detected earlier in Cyg X-2 was probably due to the shor
t time base in the RXTE data that were used, and the periodicity of 198 day
s in LMC X-3 was due to a relatively short duration of observation with HEA
O 1.