We present the analysis of the approximately three-year long Rossi X-ray Ti
ming Explorerd (RXTE) campaign for monitoring the canonical soft state blac
k-hole candidates LMC X-1 and LMC X-3. In agreement with previous observati
ons, we find that the spectra of both sources can be well-described by the
sum of a multi-temperature disc blackbody and a power law. In contrast to L
MC 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 week
s. The variability pattern observed with the RXTE All Sky Monitor reveals t
hat the variability is more complicated than the 99- or 198-d periodicity d
iscussed by Cowley et al. For typical ASM count rates, the luminosity varia
tions of LMC X-3 are due to changes of the phenomenological disc blackbody
temperature, kT(in), between similar to1 to similar to1.2 keV. During episo
des of especially low luminosity (ASM count rates less than or similar to0.
6 counts s(-1); four such periods are discussed here), kT(in) strongly decr
eases until the disc component is undetectable, and the power law significa
ntly hardens to a photon index of Gamma similar to1.8. These changes are co
nsistent 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 variabilit
y of LMC X-3 might be owing to a wind-driven limit cycle, such as that disc
ussed by Shields et al.