  We extend our previous work on the evolution of close binary systems with
misaligned orbital and spin angular momenta resulting from non-dissipative
tidal interaction to include all physical effects contributing to apsidal
motion. In addition to tidal distortion of the primary by the compact secondary
these include relativistic Einstein precession and the rotational distortion of
the primary. The influence of the precession of the line of nodes is included.
The dependence of the tidal torque on the apsidal angle $\hat\varpi$ couples
the apsidal motion to the rate of evolution of the misalignment angle $\beta$
which is found to oscillate. We provide analytical estimates for the
oscillation amplitude $\Delta\beta$ over a wide range of parameter space
confirmed by numerical integrations. This is found to be more significant near
critical curves on which $d{\hat \varpi } /dt=0$ for a specified $\beta$.
  We find that to obtain $0.1 < \Delta\beta < \sim 1,$ the mass ratio, $q >
\sim1$ the initial eccentricity should be modest, $\cos \beta < 1/\sqrt{5},$
with $\cos\beta <0 $ corresponding to retrograde rotation, initially, and the
primary rotation rate should be sufficiently large. The extended discussion of
apsidal motion and its coupled evolution to the misalignment angle given here
has potential applications to close binaries with anomalous apsidal motion as
well as transiting exoplanets such as warm Jupiters.
