We have compared the X-ray emissions of active binary stars observed at various epochs by the Einstein and ROSAT satellites in order to investigate the nature of their X-ray variability. The primary aim of this work is to determine whether or not active binaries exhibit long-term variations in X-ray emission, perhaps analogous to the observed cyclic behavior of solar magnetic activity. We find that, while the mean level of emission of the sample remains steady, comparison of different ROSAT observations of the same stars shows significant variation on timescales 2 yr, with an "effective variability" ΔI/I = 0.32 ± 0.04, where I and ΔI represent the mean emission and variation from the mean emission, respectively. A comparison of the ROSAT All-Sky Survey and later pointed observations with earlier observations of the same stars carried out with Einstein yields only marginal evidence for a larger variation (ΔI/I = 0.38 ± 0.04 for Einstein vs. ROSAT All-Sky Survey and 0.46 ± 0.05 for Einstein vs. ROSAT pointed) at these longer timescales (~10 yr), thus indicating the possible presence of a long-term component to the variability. Whether or not this long-term component is due to the presence of cyclic variability cannot be decided on the basis of existing data. However, assuming that this component is analogous to the observed cyclic variability of the Sun, we find that the relative magnitude of the cyclic component in the ROSAT passband can, at most, be a factor of 4, i.e., I_cyc/I_min < 4. This is to be compared with the corresponding but significantly higher solar value of ~10-10² derived from GOES, Yohkoh, and Solrad data. These results are consistent with the suggestions of earlier studies that a turbulent or distributive dynamo might be responsible for the observed magnetic activity on the most active, rapidly rotating stars.