A method is presented for the on-line sequential estimation (filtering) of state variables and kinetic parameters in plug flow reactors with slow catalyst decay. The essential element of this method is the approximation, for purposes of estimation only, of the distributed parameter system by a lumped parameter system. This approximation is made possible by the slow catalyst decay. The resulting sequential estimation algorithms, or filters, are computationally simple, especially the discrete filters, i.e. those based on a difference equation description. An application of two alternative discrete filters to a plug flow reactor with a first order irreversible reaction and catalyst decay has given good results. The paper includes a brief general discussion of sequential estimation and its possible applications.