  This article provides a ``local'' complementary to the previous results
concerning the local models for the moduli stacks of ``global'' $G$-shtukas.
Here we study the geometry of Rapoport-Zink spaces for local $P$-shtukas by
constructing local models for them. We further discuss certain applications,
including some results related to the theory of formal nearby cycles associated
to these spaces and the semi-simple trace of Frobenius on the corresponding
sheaves.
