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The parameter identification problem in the theory of adaptive control systems is considered from the point of view of stochastic approximation. A generalized algorithm for on-line identification of a stochastic linear discrete-time system using noisy input and output measurements is presented and shown to converge in the mean-square sense. The algorithm requires knowledge of the noise variances involved. It is shown that this requirement is a disadvantage associated with on-line identification schemes based on minimum mean-square-error criteria. The paper also presents two off-line identification schemes which utilize measurements obtained from repeated runs of the system's transient response and do not require explicit knowledge of the noise variances. These algorithms converge with probability one to the true parameter values.