  Planets around binary stars and those in multiplanet systems may experience
resonant eccentricity excitation and disruption due to perturbations from a
distant stellar companion. This "evection resonance" occurs when the apsidal
precession frequency of the planet, driven by the quadrupole associated with
the inner binary or the other planets, matches the orbital frequency of the
external companion. We develop an analytic theory to study the effects of
evection resonance on circumbinary planets and multiplanet systems. We derive
the general conditions for effective eccentricity excitation or resonance
capture of the planet as the system undergoes long-term evolution. Applying to
circumbinary planets, we show that inward planet migration may lead to
eccentricity growth due to evection resonance with an external perturber, and
planets around shrinking binaries may not survive the resonant eccentricity
growth. On the other hand, significant eccentricity excitation in multiplanet
systems occurs in limited parameter space of planet and binary semimajor axes,
and requires the planetary migration to be sufficiently slow.
