A framework for adaptive bandwidth mana ement in ATM based networks is presented. +he central concept of this approach is an adaptive estimation of the aggregate effective bandwidth required by connections carried on each link of the network. To achieve reliable results the estimation process takes into account both the trafic source declarations and the connection super osition process measurements on the network Pinks. This is done in an o timization framework procentrate on evaluation of a bandwidth reserved for possible estimation error. For this purpose we use the error covariance matrix from a linear two state KQlman lter applied for the system state timation error provides that the source parameter declarations can be more relaxed and that the source policing can be less stringent.