  Recently, a new kind of multiple zeta value level two $T({\bf k})$ (which is
called multiple $T$-values) was introduced and studied by Kaneko and Tsumura.
In this paper, we define a kind of alternating version of multiple $T$-values,
and study several duality formulas of weighted sum formulas about alternating
multiple $T$-values by using the methods of iterated integral representations
and series representations. Some special values of alternating multiple
$T$-values can also be obtained.
