The new planets were identified using 671 days of data from the NASA Kepler spacecraft 10 . As part of its mission 11 to detect Earth-like planets via the transit method, Kepler is monitoring over 2,000 eclipsing binary stars 12,13 . From these we selected a sample of 750 systems with orbital periods ranging from 0.9 to 276 days, and for which eclipses of both stars occur. For each system, we measured the eclipse times and searched for departures from strict periodicity, as would be produced by gravitational perturbations from a third body.All 750 systems were searched by eye for planetary transits, with particular attention to an 18% subset that exhibited significant differences between the periods derived from the deeper primary eclipses, and those from the shallower secondary eclipses (for details see the Supplementary Information, SI). This led to the discovery of Kepler-34 and Kepler-35, and a candidate system KOI-2939. KOI-2939 (Kepler Input Catalog 14 number 05473556) exhibited a single transit at BJD 2,454,996.995 ± 0.010 of duration 2.5 hours and depth 0.18%. The transit duration constrains the size and velocity of the third body and is consistent with a Jovian planet transiting the secondary star, but we cannot verify its planetary nature. We defer discussion for a future investigation.The stars of Kepler-34 have an orbital period of 28 days, with a period difference between primary and secondary eclipses of 4.91 ± 0.59 s. Three transits were detected (Fig 1), with the first and second being transits of the primary star, while the third is of the secondary star. Notably the transit durations are all different, ruling out the most common type of "false positive," a background eclipsing binary. Circumbinary transits naturally vary in duration as a consequence of the changing velocity of the stars. The Kepler photometry were supplemented by spectroscopic observations of the radial-velocity variations of both stars (Fig. 1f), in order to determine the orbital scale and sizes of all three bodies. The photometric and spectroscopic data were fit with a model 9,15 that accounts for the three-body gravitational dynamics and the loss of light due to eclipses and transits (see SI). The model fit confirms that the transiting body is a planet with 22% the mass of Jupiter (69 Earth masses) and 76% the radius of Jupiter (8.6 Earth radii). The primary and secondary stars are similar to the Sun. With the spectra we also measured the effective temperature and abundance of heavy elements (metallicity) of both stars. The observed stellar parameters match the Yonsei-Yale theoretical models of stellar evolution 16 for an age of 5-6 Gyr. The parameters and uncertainties are given in Table 1, with details in the SI.The stars of Kepler-35 have an orbital period of 21 days, with a period difference between primary and secondary eclipses of 1.89 ± 0.48 s. Four transits were detected (Fig. 2 b,c,d,e). The first, second, and fourth events are transits of the primary star, and the weaker third event is a transit of the secondary st...