Context : 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 .

Aims : We aim to study the properties of eccentric binary systems containing a red giant star and derive the parameters of the primary giant component .

Methods : 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 and its primary component .
Stellar evolution and its effects on the evolution of the binary system are studied from theoretical models .

Results : 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 440 days .
The results of our ongoing radial velocity monitoring program with the HERMES spectrograph reveal an eccentricity range of e = 0.2 to 0.76 .
As a case study we present a detailed analysis of KIC 5006817 , whose rich oscillation spectrum allows for a detailed seismic analysis .
From seismology we constrain the rotational period of the envelope to be at least 165 d , which is 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 300 ppm in the light curve .
Fixing the mass and radius to the asteroseismically determined values , from our binary modelling we find a value of the gravity darkening exponent that is significantly larger than expected .
Through binary modelling , we determine the mass of the secondary component to be 0.29 \pm 0.03 M _ { \odot } .

Conclusions : For KIC 5006817 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 .