Aim: Our aim is to obtain high-accuracy measurements of the physical and orbital parameters of two evolved eclipsing binary systems, and to use these measurements to study their evolutionary status. We also aim to derive distances to the systems by using a surface brightness - colour relation and compare these distances with the measurements provided by GAIA. Methods: We measured the physical and orbital parameters on both systems based on V-band and I-band photometry from OGLE, near-infrared photometry obtained with the NTT telescope and the instrument SOFI, as well as high-resolution spectra obtained at ESO 3.6m/HARPS and Clay 6.5/MIKE spectrographs. The light curves and radial-velocity curves were analysed with the Wilson-Devinney code. Results: We analysed two double-lined eclipsing binary systems OGLE-BLG-ECL-23903 and OGLE-BLG-ECL-296596 from the Optical Gravitational Lensing Experiment (OGLE) catalogue. Both systems have a configuration of two well-detached giant stars. The masses of the components ofOGLE-BLG-ECL-123903 are M_1= 2.045 $pm$ 0.027 and M_2=2.074 $pm$ 0.023 $M_odot$ and the radii are R_1=9.540 $pm$ 0.049 and R_2=9.052 $pm$ 0.060 $R_odot$. For OGLE-BLG-ECL-296596, the masses are M_1=1.093 $pm$ 0.015 and M_2=1.125 $pm$ 0.014 $M_odot$, while the radii are R_1=18.06 $pm$ 0.28 and R_2=29.80 $pm$ 0.33 $R_odot$. Evolutionary status was discussed based on the isochrones and evolutionary tracks from PARSEC and MESA codes. The ages of the systems were establishes to be around 1.3 Gyr for the OGLE-BLG-ECL-123903 and 7.7 Gyr for the OGLE-BLG-ECL-296596. We also determined the distance to both systems. For OGLE-BLG-ECL-123903 this is equal to d=2.95 $pm$ 0.06 (stat.) $pm$ 0.07 (syst.) kpc, while for the OGLE-BLG-ECL-296596 it is d=5.68 $pm$ 0.07 (stat.) $pm$ 0.14 (syst.) kpc. This is the first analysis of its kind for these unique evolved eclipsing binary systems.
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