We report the discovery of two transiting exoplanets, CoRoT-25b and CoRoT-26b, both of low density, one of which is in the Saturn mass-regime. For each star, ground-based complementary observations through optical photometry and radial velocity measurements secured the planetary nature of the transiting body and allowed us to fully characterize them. For CoRoT-25b we found a planetary mass of 0.27 ± 0.04 MJup, a radius of 1.08-0.10+0.3 RJup and hence a mean density of 0.15-0.06+0.15 g cm-3. The planet orbits an F9 main-sequence star in a 4.86-day period, that has a V magnitude of 15.0, solar metallicity, and an age of 4.5-2.0+1.8-Gyr. CoRoT-26b orbits a slightly evolved G5 star of 9.06 ± 1.5-Gyr age in a 4.20-day period that hassolar metallicity and a V magnitude of 15.8. With a mass of 0.52 ± 0.05 MJup, a radius of 1.26-0.07+0.13 RJup, and a mean density of 0.28-0.07+0.09 g cm-3, it belongs to the low-mass hot-Jupiter population. Planetary evolution models allowed us to estimate a core mass of a few tens of Earth mass for the two planets with heavy-element mass fractions of 0.52-0.15+0.08 and 0.26-0.08+0.05, respectively, assuming that a small fraction of the incoming flux is dissipated at the center of the planet. In addition, these models indicate that CoRoT-26b is anomalously large compared with what standard models could account for, indicating that dissipation from stellar heating could cause this size. The CoRoT space mission, launched on December 27th 2006, has been developed and is operated by CNES, with the contribution of Austria, Belgium, Brazil, ESA (RSSD and Science Programme), Germany and Spain. Partly based on observations obtained at the European Southern Observatory at Paranal and La Silla, Chile in programs 083.C-0690(A), 184.C-0639.