A method is presented for the real-time identification of parameters in distributed parameter systems governed by parabolic and hyperbolic partial differential equations. The method uses a finite clement technique to reduce the system's governing equation into a set of ordinary differential equations. A suitable performance index is then formed as a function of identification error. The Lyapunov design technique is used to develop proportional and integral type identification algorithms. The method can be used either on-line or off-line for identification purposes.