  We used the OGLE-II and OGLE-III photometry of red giants in the Large
Magellanic Cloud to select and study objects revealing ellipsoidal variability.
We detected 1546 candidates for long period ellipsoidal variables and 121
eclipsing binary systems with clear ellipsoidal modulation. The ellipsoidal red
giants follow a period-luminosity (PL) relationship (sequence E), and the
scatter of the relation is correlated with the amplitude of variability: the
larger the amplitude, the smaller the scatter.
  We note that some of the ellipsoidal candidates exhibit simultaneously OGLE
Small Amplitude Red Giants pulsations. Thus, in some cases the Long Secondary
Period (LSP) phenomenon can be explained by the ellipsoidal modulation.
  We also select about 1600 red giants with distinct LSP, which are not
ellipsoidal variables. We discover that besides the sequence D in the PL
diagram known before, the LSP giants form additional less numerous sequence for
longer periods. We notice that the PL sequence of the ellipsoidal candidates is
a direct continuation of the LSP sequence toward fainter stars, what might
suggest that the LSP phenomenon is related to binarity but there are strong
arguments against such a possibility.
  About 10% of the presented light curves reveal clear deformation by the
eccentricity of the system orbits. The largest estimated eccentricity in our
sample is about 0.4.
  All presented data, including individual BVI observations and finding charts
are available from the OGLE Internet archive.
