We present the analysis of an approximately 3 year long Rossi X-ray Timing Explorer (RXTE) monitoring campaign of the canonical soft state black hole candidates LMC X-1 and LMC X-3. In agreement with previous observations, we find that the spectra of both sources can be well-described by the sum of a multi-temperature disk blackbody and a power law. In contrast to LMC X-1, which does not exhibit any periodic spectral changes, we find that LMC X-3 exhibits strong spectral variability on time scales of days to weeks. The variability pattern observed with the RXTE All Sky Monitor reveals that the variability is more complicated than the 99d or 198d periodicity discussed by Cowley et al. (1991). For typical ASM count rates, the luminosity variations of LMC X-3 are due to changes of the phenomenological disk blackbody temperature, kTin, between ∼ 1 keV to ∼ 1.2keV. During episodes of especially low luminosity (ASM count rates < ∼ 0.6 counts sec −1; four such periods are discussed here), kTin strongly decreases until the disk component is undetectable, and the power la
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