  We discuss precessing compact binaries on eccentric orbit with gravastar,
black hole, neutron star, or boson star components. We derive secular evolution
equations to second post-Newtonian--order accuracy, with leading-order
spin-orbit, spin-spin, and mass quadrupole-monopole contributions. The emerging
closed system of first-order differential equations evolves the pairs of polar
and azimuthal angles of the spin and orbital angular momentum vectors together
with the periastron angle. The secular dynamics is autonomous. We confirm
numerically, that secular evolutions look like smoothed-out instantaneous
evolutions over timescales where radiation reaction is negligible. The secular
evolution of the spin polar angles and the difference of their azimuthal angles
generates a closed subsystem. We study analytically this system for the
particular cases of one spin dominating over the other and for black hole -
boson star binaries of equal masses. In the first case known large flip-flops
of the smaller spin are reproduced, when the larger spin is almost coplanar
with the orbit. We also find new, quadrupole-induced flip-flops occurring when
the neutron star with dominant spin has a quadrupolar parameter $w_1\approx 3$.
Finally we analyze the evolutions of the spin angles numerically by comparing
the cases when the black hole companion is either a gravastar, another black
hole or a boson star with identical mass. We find that both the amplitude and
period of the flip-flop are the largest, when the companion is a black hole. In
the case of a boson star companion the frequency of the flip-flop increases
significantly. Further, while in the case of gravastars and black holes a
swinging-type azimuthal evolution occurs, with the spins of the components
periodically overpassing each other, their sequence is conserved when the
companion is a boson star.
