The problem of nonparametric function fitting with the observation model y i = f (x i ) + η i , i = 1, . . . , n, is considered, where η i are independent random variables with zero mean value and finite variance, and form a random sample from a distribution with density ∈ L 1 [a, b] and are independent of the errors η i , i = 1, . . . , n. The asymptotic properties of the estimator f N (n) (x) = N (n) k=1 c k e k (x) for f ∈ L 2 [a, b] and c N (n) = ( c 1 , . . . , c N (n) ) T obtained by the

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... east squares method as well as the limits in probability of the estimators c k , k = 1, . . . , N , for fixed N , are studied in the case when the functions e k , k = 1, 2, . . . , forming a complete orthonormal system in L 2 [a, b] are analytic. 1991 Mathematics Subject Classification: Primary 62G07, 62F12.