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 99 d or 198 d periodicity discussed by Cowley et al . [ 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 , kT _ { in } , between \sim 1 keV to \sim 1.2 keV . During episodes of especially low luminosity ( ASM count rates \mathrel { \hbox to 0.0 pt { \raise 2.1973 pt \hbox { $ < $ } } { \lower 2.1973 pt \hbox { $ \sim$% } } } 0.6 counts sec ^ { -1 } ; four such periods are discussed here ) , kT _ { in } strongly decreases until the disk component is undetectable , and the power law significantly hardens to a photon index of \Gamma \sim 1.8 . These changes are consistent with state changes of LMC X-3 from the soft state to the canonical hard state of galactic black holes . We argue that the long term variability of LMC X-3 might be due to a wind-driven limit cycle , such as that discussed by Shields et al . [ Shields et al . 1986 ] .