  We apply the technique of affine Hecke algebras to the invariant theory of
the "queer" Lie superalgebra $q_N$. We give explicit formulas for the elements
of a distinguished basis in the centre of $U(q_N)$, determined by "vanishing"
conditions. We evaluate the corresponding differential operators on
$C^{N|N}\otimes C^{M|M}$. In particular, we obtain an analogue for $q_N$ of the
classical Capelli identity.
