The Asymptotic Theory of ideals originated with the investigation in noetherian ringAof the Samuel numbers ⊢I(J) and [wbar]I(J) associ-ated to each pair (I, J) of nonnilpotent ideals having the same radical where, the limit being reached from below and. The number [wbar]I(J) is defined in a symetric situation. As an answer of a question raised by Samuel, Nagata has shown that the set of deviationsis bounded. Here we extend these numbers to pairs (f,g), wheref= (In) andg= (Jn) are filtrations onA, as follows:, wheref(r) is filtration (Inr). We prove in particular that iffandgare separated, nonnilpotent, stronglyAPfiltrations and suchthen the deviation sequenceis bounded in R+. A similar study is done concerning the sequenceandbf(g) = ∞ if the last set is empty.