  We report the discovery of two distinct types of ellipsoidal binary systems
occupying, so called, sequence E on the period-luminosity (P-L) diagram. We
propose that steeper P-L relation is composed of giant-dwarf binaries, while
the other consists of giant-giant binary systems. Analysis is based on a sample
of 5334 objects, which we select from the OGLE-III survey data toward the the
Large Magellanic Cloud. We show that one of the components of ellipsoidal
binaries is typically either a Red Clump or a Red Giant Branch star, which
leads to clear separation split of the sequence E at P = 40 d. In its
short-period part, we identify two subsequences corresponding to the two types
of binary systems (E2 and E3), while in the longer-period part the two groups
merge forming a single subsequence E1. We extract a group of 271 ellipsoidal
systems with eccentric orbits, from our sample. We present the
period-luminosity relation they follow.
