We present a study of the intraday variability behaviour of two samples of x-ray selected BL Lac objects, the EMSS and EXOSAT samples consisting of 22 and 11 sources, respectively. In both samples we were able to detect intraday variability in less than 40% of the sources only. The duty cycle (the fraction of time, when a BL Lac object is variable) in x-ray selected BL Lac objects is 0.4 or less. The typical peak-to-peak amplitudes of the variability are 10%. Typical time-scales and an activity parameter for our variable BL Lac objects were inferred from structure function and autocorrelation function analyses. In only 4 BL Lac objects we were able to measure a characteristic time-scale, which was in the range between 1.3 and 2.7 days. Comparison with our previous study of a complete sample of radio-selected BL Lac objects from the 1 Jy catalogue shows that x-ray and radio-selected BL Lac objects differ in their duty cycle by a factor of 2 and the typical peak-to-peak amplitudes by a factor of 3. The observed time-scales are similar. We also found that the same mechanism may be responsible for the observed variability in the x-ray selected and radio-selected BL Lac objects. The expectations of the various schemes linking x-ray selected and radio-selected BL Lac objects have been compared to our observations. Consistency is found for a scenario, where x-ray selected BL Lac objects have on average stronger magnetic fields and are seen under relatively larger viewing angles than the radio-selected BL Lac objects. However, the suggestion that x-ray selected BL Lac objects have decelerating jets and radio-selected BL Lac objects accelerating jets can also not be ruled out.
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