  Thirty eight long-period (P>10 days), apparently contact binary stars
discovered by the OGLE-II project in the SMC appear to be Beta Lyrae-type
systems with ellipsoidal variations of the cool components dominating over
eclipse effects in the systemic light variations and in the total luminosity. A
new period-luminosity- color (PLC) relation has been established for these
systems; we call it the PLC-beta relation, to distinguish it from the Cepheid
relation. Two versions of the PLC-beta relation - based on the (B-V)0 or (V-I)0
color indices - have been calibrated for 33 systems with (V-I)0>0.25 spanning
the orbital period range of 11 to 181 days. The relations can provide
maximum-light, absolute-magnitude estimates accurate to epsilon-M_V~0.35 mag.
within the approximate range -3<M_V<+1. In terms of their number in the SMC,
the long-period Beta Lyrae-type binaries are about 50 times less common than
the Cepheids. Nevertheless, their large luminosities coupled with continuous
light variations make these binaries very easy to spot in nearby galaxies, so
that the PLC-beta relation can offer an auxiliary and entirely independent
method of distance determination to nearby stellar systems rich in massive
stars. The sample of the long-period Beta Lyrae systems in the SMC analyzed in
this paper is currently the best defined and uniform known sequence of such
binaries.
