  Let ${\frak M}_n$ be the set of equivariant unoriented cobordism classes of
all $n$-dimensional 2-torus manifolds, where an $n$-dimensional 2-torus
manifold $M$ is a smooth closed manifold of dimension $n$ with effective smooth
action of a rank $n$ 2-torus group $({\Bbb Z}_2)^n$. Then ${\frak M}_n$ forms
an abelian group with respect to disjoint union. This paper determines the
group structure of ${\frak M}_n$ and shows that each class of ${\frak M}_n$
contains a small cover as its representative in the case $n=3$.
