  We develop a semi-analytical approach, based on the post-Newtonian expansion
and on the affine approximation, to model the tidal deformation of neutron
stars in the coalescence of black hole-neutron star or neutron star-neutron
star binaries. Our equations describe, in a unified framework, both the system
orbital evolution, and the neutron star deformations. These are driven by the
tidal tensor, which we expand at 1/c^3 post-Newtonian order, including spin
terms. We test the theoretical framework by simulating black hole-neutron star
coalescence up to the onset of mass shedding, which we determine by comparing
the shape of the star with the Roche lobe. We validate our approach by
comparing our results with those of fully relativistic, numerical simulations.
