The kinematics of 237 chromospherically active binaries (CABs) were studied. The sample is heterogeneous with different orbits and physically different components from F to M spectral-type main-sequence stars to G and K giants and supergiants. The computed U, V, W space velocities indicate that the sample is also heterogeneous in velocity space. That is, both kinematically younger and older systems exist among the non-evolved main sequence and the evolved binaries containing giants and subgiants. The kinematically young (0.95 Gyr) subsample (N = 95), which is formed according to the kinematical criteria of moving groups, was compared with the rest (N = 142) of the sample (3.86 Gyr) to investigate any observational clues of binary evolution. Comparing the orbital period histograms between the younger and older subsamples, evidence was found supporting the finding of Demircan that the CABs lose mass (and angular momentum) and evolve towards shorter orbital periods. The evidence of mass loss is noticeable on the histograms of the total mass (M-h + M-c), which is compared between the younger (only N = 53 systems available) and older subsamples (only N = 66 systems available). The orbital period decrease during binary evolution is found to be clearly indicated by the kinematical ages of 6.69, 5.19 and 3.02 Gyr which were found in the subsamples according to the period ranges of log P less than or equal to 0.8, 0.8 < log P &LE; 1.7 and 1.7 < log P less than or equal to 3, respectively, among the binaries in the older subsample.