We investigate interpolation and extrapolation properties of partial clones of infinite-valued logic functions. Maximal local partial clone on an infinite set E is characterized by conditions on its intersections with the full partial clone on every finite subset A \subset E, {\rm{2 }} \le \left| A \right| \le \infty. Next the criterion is given for a finite domain partial operation of a local partial clone to be extendable to everywhere defined operation from the same clone. Similar criterion is also given for a local partial clone to be extendable. Finally, extendibility conditions for partial orders are obtained so that the clones of their partial n-endomorphisms become extendable.