Formally, a signal is said to have the finite variability property, unless the sequence is infinite and formula_11 is bounded. Intuitively, the finite variability property state that there is not an infinite number of change in a finite time. Having the finite variability property is similar to the notion of being non-Zeno for a timed word.. The notion of bounded variability is a restriction to the notion of finite variability. A signal has the bounded variability property if there exists a lower bound between the beginning of two intervals with the same letter. Before giving a formal definition, we give an example of signal which is finitely variable but not boundedly variable. Take the alphabet formula_12. Take the interval formula_1 which sends the reals of the form formula_14 with formula_15 and formula_16 to formula_17 and every other reals to formula_18. During each finite time interval, the letter change a finite number of time. Thus this signal is finitely variable. However, the distance between two successive occurrences of the letter formula_17 is arbitrarily small. Thus it does not have the bounded variability property. Let a sequence formula_20. If formula_21 for each integer formula_8, then the sequence is said to have the bounded variability property if there exists a real formula_23 such that, for each formula_24 with formula_25 such that there exists no formula_26 with formula_27 and formula_28 then the difference between the lower bound of formula_29 and of formula_30 is at least formula_31. Note that each sequence formula_1 is equivalent to a sequence formula_33 in which two successive letters are distinct. The sequence formula_1 is said to have the bounded variability property if and only if formula_33 has the bounded variability property. A set of signal is said to has the bounded variability property if the above mentioned lower bound formula_31 can be chosen to be the same for each signal of the set. We know give main reason to consider signals with bounded variabilities. Assume we need to create a system, such as a signal automaton, which need to recall everything which occurred in the last time units. If we know that the signal is boundedly variable, we can compute an upper bound on the number of action which occurred during one time unit. Thus, we can create such a system and ensure that it only requires a finite memory. For example, for an arbitrary predicate formula_37, the signal stating whether the statement "formula_38 holds sometime in the next time unit" holds has the bounded variability property.