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Gaussian processes that are multifractional are studied in this paper. By multifractional processes we mean that they behave locally like a fractional Brownian motion, but the fractional index is no more a constant: it is a function. We introduce estimators of this multifractional function based on discrete observations of one sample path of the process and we study their asymptotical behaviour as the mesh decreases to zero. Key-words: Gaussian processes, identication, multifractional function. AMS classication (1991): 60G15,60G17,62G05