  Nazarov \cite{Nazarov:brauer} introduced an infinite dimensional algebra,
which he called the \textit{affine Wenzl algebra}, in his study of the Brauer
algebras. In this paper we study certain ``cyclotomic quotients'' of these
algebras. We construct the irreducible representations of these algebras in the
generic case and use this to show that these algebras are free of rank
$r^n(2n-1)!!$ (when $\Omega$ is $\bu$--admissible). We next show that these
algebras are cellular and give a labelling for the simple modules of the
cyclotomic Nazarov--Wenzl algebras over an arbitrary field. In particular, this
gives a construction of all of the finite dimensional irreducible modules of
the affine Weyl algebra (when $\Omega$ is admissible).
