  It has been suggested that both X-ray bursters and millisecond radio pulsars
may be strange (quark) stars, rather than neutron stars. Confirming (or
rejecting) this suggestion may require knowing what role strong-field effects
of general relativity play in the accretion flow of the compact X-ray source in
low-mass X-ray binaries (LMXBs). We discuss the range of rotational and orbital
frequencies, and of masses expected in various models of strange stars, and
compare them with observational constraints, suggested by the observed
frequencies of kHz QPOs. We explain why future observations of transients (such
as SAX J~1808.4-3658) may be crucial to understanding the precise nature of the
accreting source. For flattened (e.g., rapidly rotating) distributions of
matter, an innermost (marginally) stable orbit may be present even if
relativistic effects are negligible. Depending on the stellar rotation rate,
the same value of orbital frequency in the innermost stable orbit (say, 0.9
kHz) can correspond to a star of mass equal to $2.4M_\odot$, $1.4M_\odot$,
$0.1M_\odot$, $0.01M_\odot$, or less.
