A new practical method, hereby called the ‘moment functional method’, is presented for the identification of the parameters of distributed parameter systems characterized by either the one-dimensional wave or diffusion equation. The method is extended to include systems characterized by a one-dimensional diffusion equation with a coefficient which is a polynomial in time. In this case the method determines the coefficients in the polynomial. The feasibility of the method lies in the on-line generation of linear time-invariant algebraic equations in the unknown system parameters by means of two Poisson filter chains which are fed from three points along the distributed system. The results of simulation studies are presented to illustrate the applicability of the method.