There has been a great deal of research activity in the area of identification of distributed parameter systems over the past two decades. An extensive treatment of off-line schemes ( e.g. , output least squares, estimation error, etc. ) together with a comprehensive survey of the literature can be found in the monograph by Banks and Kunisch [4] . In the case of on-line, or adaptive, schemes, the available literature is less extensive and more recent ( Isermann et al . [7] ). The on-line methods give estimates recursively as the measurements are obtained within the time limit imposed by the sampling period. These include recursive projection algorithm ( Baumeister et al. [5] ), recursive least squares algorithm ( Glentis et al . [6] ), on-line excitation algorithms ( Ludwig et al. [8] ), etc . In this paper an equivalent 2nd order dynamical system is formulated from a given trajectory representing the pattern to be recognised and simulated in order to estimate the parameters for hierarchical distributed systems using 1st and 2nd order dynamics. Recommendations for the best estimation strategy are given.