This paper is the second in the planned series of investigations. We present new radial velocities and photometric observations of V2080 Cyg and V2365 Oph. New UBV photometric data and radial velocities were analysed for the systems' parameters. While V2080 Cyg consists of two nearly equal F-type main-sequence stars, V2365 Oph has two different components, namely an early A-type primary and a G-type secondary star. New ephemerides are calculated for both systems. The masses of the component stars have been derived as 1.19 +/- 0.02 and 1.16 +/- 0.02 M(circle dot) for V2080 Cyg and 1.97 +/- 0.02 and 1.06 +/- 0.01 M(circle dot) for V2365 Oph. The effective temperatures and reddening of the systems have been estimated from Johnson wide-band UBV photometric calibrations. The radii have been measured by simultaneous fitting the UBV light curves using Wilson - Devinney code and are 1.60 +/- 0.01 R(circle dot) for both components of V2080 Cyg and 2.19 +/- 0.01 and 0.934 +/- 0.004 R(circle dot) for V2365 Oph. The absolute parameters of the stars in both systems lie within the same ranges in the mass-radius, mass-effective temperature, mass-luminosity and luminosity-effective temperature planes as in detached Algol systems. A comparison between the properties of the systems of interest and the predictions of theoretical evolutionary models is undertaken in the log g - logT(eff), log R - logM and radius-log age diagrams. The model predictions match the measured properties of V2080 Cyg for an age of about 5.6 Gyr and a 'solar' metal abundance (Z=0.019), indicating the components near the end of their core hydrogen-burning phases. However, the position of the components of V2365 Oph on the Hertzsprung - Russell (HR) diagram is best reproduced with evolutionary models for somewhat metal-deficient (Z=0.004) stars. We found an age of about 700 Myr, with the primary component slightly evolved off the zero-age main-sequence and the secondary one still very close to it. From the basic stellar parameters we have also redetermined the distances to V2080 Cyg and V2365 Oph as 78 1 and 251 8 pc, which are in agreement with, and more accurate than, Hipparcos values. The observations show that at least one of the components of V2365 Oph is an intrinsic variable with a period and peak-to-peak amplitude of 0.07 d and 0.05 mag, respectively. In accordance with its position in the HR diagram, the primary component should be considered as a delta Scuti star and it is believed to be the variable star in the system.