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In this paper a class of system identification problems of nonparametric type is considered. Specifically, given an unknown deterministic system, some basic structural aspects related to the problem of estimating its weighting function are discussed. The model adopted for the system input-output relation is general enough to cover a number of situations ranging from problems of identification of linear time-invariant systems to those where the system is nonlinear and time varying. The emphasis is on establishing what, in principle, can be recovered of the system weighting function through a noiseless identification process and the ultimate limitations imposed by the presence of observation or measurement noise.