Obliquity variability could play an important role in the climate and habitability of a planet . Orbital modulations caused by planetary companions and the planet ’ s spin axis precession due to the torque from the host star may lead to resonant interactions and cause large-amplitude obliquity variability . Here we consider the spin axis dynamics of Kepler-62f and Kepler-186f , both of which reside in the habitable zone around their host stars . Using N -body simulations and secular numerical integrations , we describe their obliquity evolution for particular realizations of the planetary systems . We then use a generalized analytic framework to characterize regions in parameter space where the obliquity is variable with large amplitude . We find that the locations of variability are fine-tuned over the planetary properties and system architecture in the lower-obliquity regimes ( \lesssim 40 ^ { \circ } ) . As an example , assuming a rotation period of 24 hr , the obliquities of both Kepler-62f and Kepler-186f are stable below \sim 40 ^ { \circ } , whereas the high-obliquity regions ( 60 ^ { \circ } -90 ^ { \circ } ) allow moderate variabilities . However , for some other rotation periods of Kepler-62f or Kepler-186f , the lower-obliquity regions could become more variable owing to resonant interactions . Even small deviations from coplanarity ( e.g . mutual inclinations \sim 3 ^ { \circ } ) could stir peak-to-peak obliquity variations up to \sim 20 ^ { \circ } . Undetected planetary companions and/or the existence of a satellite could also destabilize the low-obliquity regions . In all cases , the high-obliquity region allows for moderate variations , and all obliquities corresponding to retrograde motion ( i.e . > 90 ^ { \circ } ) are stable . Keywords : Exoplanets : dynamics – Exoplanets : habitability – Methods : numerical – Methods : analytical