This thesis considers the parameter identification problem for systems governed by partial differential equations. The various identification methods sire grouped into three disjoint classes namely: "Direct Methods", "Reduction to a Lumped Parameter System", and "Reduction to an Algebraic Equation". The major subject investigated here is concerned with the applicability of stochastic approximation algorithms for identifying distributed parameter systems (DPS) operating in a stochastic environ­ment, where no restriction on probability distributions is imposed. These algorithms are used as a straightforward identification procedure, converge to the real value of the parameters with probability one, and are suitable for on-line applications. In this way, a new identification method is developed for DPS described by linear models, driven by random inputs, and observed through noisy measurements. The very real case of noisy observations taken at a limited number of discrete points located in the spatial domain is considered. The proposed identifica­tion method assumes that a previous system classification has been performed, such that the model to be identified is known up to a set of space-varying parameters, where extraneous terms may be included.