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We characterize Lie -Backlund vector fields in infinite dimensional jetbundles $J^\infty(\mathbb{R}^n, \mathbb{R}^m)$ that can be exponentiated toflows with each component depending on a finite set of variables. We show thatfor $m=1$ each such field is an extension of one in a finite dimensional jetspace. For $m>1$ this is no longer the case and we give necessary andsufficient conditions for exponentiation. Non-trivial examples are provided for$(n,m)=(1,2)$.

Exponentiable Lie-Backlund vector fields in $J^\infty(\mathbb{R}^n, \mathbb{R}^m)$