  As shown by Mennickent, et al(2003), a subset of the blue variable stars in
the Large Magellanic Cloud exhibit brightness variability of small amplitude in
the period range 2.4 to 16 days as well as larger amplitude variability with
periods of 140 to 600 days, with a remarkably tight relation between the long
and the short periods. Our re-examination of these objects has led to the
discovery of additional variability. The Fourier spectra of 11 of their 30
objects have 3 or 4 peaks above the noise level and a linear relation of the
form f_a = 2(f_b - f_L) among three of the frequencies. An explanation of this
relation requires an interplay between the binary motion and that of a third
object. The two frequency relations together with the Fourier amplitude ratios
pose a challenging modeling problem.
