  We use Fra\" iss\'e theoretic methods to construct several universal and
ultrahomogeneous Polish metric structures. Namely, universal and
ultrahomogeneous Polish metric space equipped with countably many closed
subsets of its powers, universal and ultrahomogeneous Polish metric space
equipped with a closed subset of the product of itself and some fixed compact
metric space, and universal and ultrahomogeneous Polish metric space equipped
with an L-Lipschitz function, for an arbitrary positive L, to some fixed Polish
metric space. These results are direct generalization of the classical result
of P. Urysohn. Possible applications are discussed.
