In this paper, we present a spectroscopic study of six double-lined binaries, five of which were recently discovered in a high-resolution spectroscopic survey of optical counterparts of stellar X-ray sources. Thanks to high-resolution spectra acquired with CAOS spectropolarimeter during 7 yr, we were able to measure the radial velocities of their components and determine their orbital elements. We have applied our code COMPO2 to determine the spectral types and atmospheric parameters of the components of these spectroscopic binaries and found that two of these systems are composed of main-sequence stars, while the other four contain at least one evolved (giant or subgiant) component, similar to other well-known RS CVn systems. The subtraction of a photospheric template built up with spectra of non-active stars of the same spectral type as those of the components of each system has allowed us to investigate the chromospheric emission that fills in the H α cores. We found that the colder component is normally the one with the largest H α emission. None of the systems show a detectable Li Iλ6708 line, with the exception of TYC 4279-1821-1, which exhibits high photospheric abundances in both components. Photometric time-series from the literature allowed us to assess that the five systems with a nearly circular orbit have also photometric periods close or equal to the orbital ones, indicating spin-orbit synchronization. For the system with a highly eccentric orbit, a possible pseudo-synchronization with the periastron velocity is suggested.