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We investigate the dynamics of compact binaries on timescales where the back-reaction of gravitational waves is negligible, but the evolution spans over a few precessional periods. This justifies the discussion through secular dynamics, obtained by integration over the radial period. The secular evolution refers to the polar and azimuthal angles of the spins and of the orbital angular momentum vectors together with the periastron angle. We monitor the spin directions when one or both axes undergo significant changes. We show how the quadrupole parameter of the quadrupole-monopole interaction could essentially modify the flip-flop effect.