Our main aim is the first detailed analysis of the two eclipsing binaries V456 Oph and V490 Cyg .
The system V456 Oph has been studied both photometrically via an analysis of its light curve observed by the INTEGRAL/OMC and by the period analysis of all available times of minima .
V490 Cyg has been studied by means of a period analysis only .
Many new times of minima for both systems have recently been observed and derived .
This allows us for the first time to study in detail the processes that affect both binaries .
The main result is the discovery that both systems have eccentric orbits .
For V456 Oph we deal with the eccentric eclipsing binary system with the shortest orbital period known ( about 1.016 day ) , while the apsidal motion period is about 23 years .
V490 Cyg represents the eclipsing system with the shortest apsidal motion period ( about 18.8 years only ) .
The two components of V456 Oph are probably of spectral type F. We compare and discuss the V456 Oph results from the light curve and the period analysis , but a more detailed spectroscopy is needed to confirm the physical parameters of the components more precisely .