In Constant temperature the troglobite beetles Aphaenops cerberus and pluto, Geotrechus orpheus and Speonomus diecki are aperiodically active. By periodogram analysis neither circadian nor ultradian or infradian periodic components can be found. Moreover there are no relevant correlations between the lengths of successive activity bursts and rest pauses. Consequently the activity patterns are stochasticly structured. In cases with constancy of activity respectively rest behaviour the probabilities for the transition from activity to rest and from rest to activity are computed using the Frequency histograms of lengths of activity bursts and rest pauses. The transition probability is time-invariant if the observed histogram can be approximated to the negative exponential function. Y=ae-fx . The transition probability increases continuously if the observed histogram can be approximated to the Poisson or normal function. -74% of the investigated frequency histograms of the length of activity bursts and 57% of the histograms of the lengths of rest pauses can be approximated to one of the tested functions. Aphaenops and Geotrechus specimens do not react to changes of the illumination intensity. Conversely temperature cycles induce distinct activity periodicities. In Aphaenops the mean length of activity bursts is -on the average - less temperature dependent than the mean length of rest pauses. Moreover, in this species the mean length of bursts is weakly negatively correlated with the mean length of pauses. The evolution and adaptive reactions of the random mechanism of activity control in troglobite animals are discussed.