  In a preceding paper the theory of nonsymmetric Macdonald polynomials taking
values in modules of the Hecke algebra of type $A$ (Dunkl and Luque SLC 2012)
was applied to such modules consisting of polynomials in anti-commuting
variables, to define nonsymmetric Macdonald superpolynomials. These polynomials
depend on two parameters $\left( q,t\right) $ and are defined by means of a
Yang-Baxter graph. The present paper determines the values of a subclass of the
polynomials at the special points $\left( 1,t,t^{2},\ldots\right) $ or$\left(
1,t^{-1},t^{-2},\ldots\right) $. The arguments use induction on the degree and
computations with products of generators of the Hecke algebra. The resulting
formulas involve $\left( q,t\right)$-hook products. Evaluations are also found
for Macdonald superpolynomials having restricted symmetry and antisymmetry
properties.
