  We present a study of OGLE light curves of red giant stars exhibiting long
secondary periods (LSPs) - an enigmatic phenomenon commonly observed in stars
on the upper red giant branch and asymptotic giant branch. We show that the
light curves of LSP stars are essentially identical to those of the spotted
variables with one dark spot on their photospheres. Such a behavior can be
explained by a presence of a dusty cloud orbiting the red giant together with a
low-mass companion in a close, circular orbit. We argue that the binary
scenario is in agreement with most of the observational properties of LSP
variables, including non-sinusoidal shapes of their radial velocity curves.
