The experimental data on two quasi‐particle (2qp) rotational bands of even‐even rare‐earth nuclei reveal significant odd‐even staggering in both K+=(&OHgr;1+&OHgr;2) and K=‖&OHgr;1−&OHgr;2‖ bands. An empirical rule is proposed for the phase of staggering and is checked with the experimental data. More complexities are exhibited by these rotational bands as compared to odd‐odd nuclei which are evidenced in the form of anomalous behavior seen in the cases where data are known up to higher spins.