We analyse the evolution of a mildly inclined circumbinary disc that orbits an eccentric orbit binary by means of smoother particle hydrodynamic ( SPH ) simulations and linear theory . We show that the alignment process of an initially misaligned circumbinary disc around an eccentric orbit binary is significantly different than around a circular orbit binary and involves tilt oscillations . The more eccentric the binary , the larger the tilt oscillations and the longer it takes to damp these oscillations . A circumbinary disc that is only mildly inclined may increase its inclination by a factor of a few before it moves towards alignment . The results of the SPH simulations agree well with those of linear theory . We investigate the properties of the circumbinary disc/ring around KH 15D . We determine disc properties based on the observational constraints imposed by the changing binary brightness . We find that the inclination is currently at a local minimum and will increase substantially before setting to coplanarity . In addition , the nodal precession is currently near its most rapid rate . The recent observations that show a reappearance of Star B impose constraints on the thickness of the layer of obscuring material . Our results suggest that disc solids have undergone substantial inward drift and settling towards to disc midplane . For disc masses \sim 0.001 M _ { \odot } , our model indicates that the level of disc turbulence is low \alpha \ll 0.001 . Another possibility is that the disc/ring contains little gas .