  The paper is dedicated to the problem of adding a modality to the
\Lukasiewicz many-valued logics in the purpose of obtaining completeness
results for Kripke semantics. We define a class of modal many-valued logics and
their corresponding Kripke models and modal many-valued algebras. Completeness
results are considered through the construction of a canonical model.
Completeness is obtained for modal finitely-valued logics but also for a modal
many-valued system with an infinitary deduction rule. We introduce two classes
of frames for the finitely-valued logics and show that they define two distinct
classes of Kripke-complete logics.
