  The unparalleled photometric data obtained by NASA's Kepler space telescope
led to an improved understanding of red giant stars and binary stars.
Seismology allows us to constrain the properties of red giants. In addition to
eclipsing binaries, eccentric non-eclipsing binaries, exhibiting ellipsoidal
modulations, have been detected with Kepler. We aim to study the properties of
eccentric binary systems containing a red giant star and derive the parameters
of the primary giant component. We apply asteroseismic techniques to determine
masses and radii of the primary component of each system. For a selected
target, light and radial velocity curve modelling techniques are applied to
extract the parameters of the system. The effects of stellar on the binary
system are studied. The paper presents the asteroseismic analysis of 18
pulsating red giants in eccentric binary systems, for which masses and radii
were constrained. The orbital periods of these systems range from 20 to
440days. From radial velocity measurements we find eccentricities between e=0.2
to 0.76. As a case study we present a detailed analysis of KIC5006817. From
seismology we constrain the rotational period of the envelope to be at least
165 d, roughly twice the orbital period. The stellar core rotates 13 times
faster than the surface. From the spectrum and radial velocities we expect that
the Doppler beaming signal should have a maximum amplitude of 300ppm in the
light curve. Through binary modelling, we determine the mass of the secondary
component to be 0.29$\pm$0.03\,$M_\odot$. For KIC5006817 we exclude
pseudo-synchronous rotation of the red giant with the orbit. The comparison of
the results from seismology and modelling of the light curve shows a possible
alignment of the rotational and orbital axis at the 2$\sigma$ level. Red giant
eccentric systems could be progenitors of cataclysmic variables and hot
subdwarf B stars.
