Demazure slices are associated graded pieces of infinite-dimensional version of Demazure
modules for affine Lie algebras. In this talk, we review (1) Demazure slices for other types and
(2) usual finite dimensional Demazure modules of type $A_{2l}^{(2)}$. Then we explain a relation
between graded characters of Demazure slices for $A_{2l}^{(2)}$ and specialized nonsymmetric
Macdonald-Koornwinder polynomials.