A planet ’ s climate can be strongly affected by its orbital eccentricity and obliquity . Here we use a 1-dimensional energy balance model modified to include a simple runaway greenhouse ( RGH ) parameterization to explore the effects of these two parameters on the climate of Earth-like aqua planets —completely ocean-covered planets—orbiting F- , G- , K- , and M-dwarf stars . We find that the range of instellations for which planets exhibit habitable surface conditions throughout an orbit decreases with increasing eccentricity . However , the appearance of temporarily habitable conditions during an orbit creates an eccentric habitable zone ( EHZ ) that is sensitive to orbital eccentricity and obliquity , planetary latitude , and host star spectral type . We find that the fraction of a planet ’ s orbit over which it exhibits habitable surface conditions is larger on eccentric planets orbiting M-dwarf stars , due to the lower broadband planetary albedos of these planets . Planets with larger obliquities have smaller EHZs , but exhibit warmer climates if they do not enter a snowball state during their orbits . We also find no transient runaway greenhouse state on planets at all eccentricities . Rather , planets spend their entire orbits either in a RGH or not . For G-dwarf planets receiving 100 % of the modern solar constant and with eccentricities above 0.55 , an entire Earth ocean inventory can be lost in 3.6 Gyr . M-dwarf planets , due to their larger incident XUV flux , can become desiccated in only 690 Myr with eccentricities above 0.38 . This work has important implications for eccentric planets that may exhibit surface habitability despite technically departing from the traditional habitable zone as they orbit their host stars .