Many of the recently discovered extrasolar giant planets move around their stars on highly eccentric orbits, and some with e [ges ] 0·7. Systems with planets within or near the habitable zone (HZ) will possibly harbour life on terrestrial-type moons if the seasonal temperature extremes resulting from the large orbital eccentricities of the planets are not too severe. Here we use a three-dimensional general-circulation climate model and a one-dimensional energy-balance model to examine the climates of either bound or isolated earths on extremely elliptical orbits near the HZ. While such worlds are susceptible to large variations in surface temperature, long-term climate stability depends primarily on the average stellar flux received over an entire orbit, not the length of the time spent within the HZ.