  We present the analysis of an RXTE monitoring campaign of the canonical soft
state black hole candidates LMC X-1 and LMC X-3. In contrast to LMC X-1, which
does not exhibit any periodic spectral changes, we find that LMC X-3 exhibits
stron spectral variability on time scales of days to weeks. For typical RXTE
ASM count rates, the luminosity variations of LMC X-3 are due to changes of the
phenomenological disk blackbody temperature. During episodes of especially low
luminosity (ASM count rates < 0.6 counts/sec), kT strongly decreases and the
power law significantly hardens to a photon index of ~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 hole candidates. We argue that the long term
variability of LMC X-3 might be due to a wind-driven limit cycle such as
discussed by Shields et al. (1986)
