Multistable processes are tangent at each point to a stable process, but where the index of stability and the index of localisability varies along the path. In this work, we give two estimators of the stability and the localisability functions, and we prove the consistency of those two estimators. We illustrate these convergences with two examples, the Levy multistable process and the Linear Multifractional Multistable Motion. Note that when the function α is constant, then (2.2) is just the

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... guson -Klass -LePage series representation of a stable random variable (see [1, 7, 10, 11, 15] and [16, Theorem 3.10.1] for specific properties of this representation). Multistable processes Multistable processes are obtained by taking diagonals on X defined in (2.2), i.e. Y (t) = X(t, t). (2.3) Indeed, as shown in Theorems 3.3 and 4.5 of [8], provided some conditions are satisfied both by X and by the function f , Y will be a localisable process whose local form is a 3