We present and analyse high-resolution optical spectra of two Algol binaries, namely S Equ and KO Aql, obtained with the echelle spectrograph at Catania Astrophysical Observatory. New accurate radial velocities (RVs) for the hotter primary components are obtained. Thanks to the cross-correlation procedure, we were able to measure, for the first time to our knowledge, RVs also for the cool secondary components of S Equ and KO Aql. By combining the parameters obtained from the solution of the RV curves with those obtained from the light-curve analysis, reliable absolute parameters of the systems have been derived. The rotational velocity of the hotter components of S Equ and KO Aql has been measured and it is found that the gainers of both systems rotate about 30 per cent faster than synchronously. This is likely due to mass transfer across the Lagrangian L-1 point from the cooler to the hotter component. The lower luminosity of the mass-gaining components of these systems compared to normal main-sequence stars of the same mass can also be an effect of the mass transfer. The H alpha profiles were analysed with the 'synthesis and subtraction' technique and reveal clear evidence of mass transfer and accretion structures. In both systems, especially before the primary eclipses and afterwards, we clearly observed extra absorption lines. From the integrated absorption and the RV variations of these features, we found that the mass accretion is very dense around the impact region of the hotter components. A double-peaked emission in the spectra of S Equ was seen outside the eclipses. One of these peaks is likely originated in a region between the centre of mass and the cooler component, which is occupied by the flowing matter. Furthermore, the H alpha difference spectra of S Equ and KO Aql also display emission features, which should be arising from the magnetic activity of the cooler components.