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After Crouch , we clarify the relation between minimal realizations Sussmann - and weakly minimal realizations Hermann and Krener  of a given input-output mapping in the analytic case. For a given input-output mapping, all the weakly minimal analytic realizations are classified. Our result, applied to realization theory, is exactly Crouch's one, and can be derived from Sussmann's paper . Otherwise, it is closely related to other works of Krener  and Hermann and Krener . Our contribution is essentially a presentation of the above-mentioned results in a general unified manner.