LMC X-1 and LMC X-3 are the only known persistent stellar-mass black-hole c
andidates that have almost always shown spectra that are dominated by a sof
t, thermal component. We present here results from 170-ks-long Rossi X-ray
Timing Explorer (RXTE) observations of these objects, taken in 1996 Decembe
r, where their spectra can be described by a disc blackbody plus an additio
nal soft (Gamma similar to2.8) high-energy power law (detected up to energi
es of 50 keV in LMC X-3). These observations, as well as archival Advanced
Satellite for Cosmology and Astrophysics (ASCA) observations, constrain any
narrow Fe line present in the spectra to have an equivalent width less tha
n or similar to 90 eV. Stronger, broad lines (approximate to 150 eV EW, sig
ma approximate to1 keV) are permitted. We also study the variability of LMC
X-1. Its X-ray power spectral density (PSD) is approximately proportional
to f(-1) between 10(-3) and 0.3 Hz with a root-mean-square (rms) variabilit
y of approximate to7 per cent. At energies >5 keV, the PSD shows evidence o
f a break at f >0.2 Hz, possibly indicating an outer disc radius of less th
an or similar to 1000 GMc(2) in this likely wind-fed system. Furthermore, t
he coherence function gamma (2)( f), a measure of the degree of linear corr
elation between variability in the >5 keV band and variability in the lower
energy bands, is extremely low (less than or similar to 50 per cent). We d
iscuss the implications of these observations for the mechanisms that might
be producing the soft and hard X-rays in these systems.