  Let $G$ be a graph. A total dominating set of $G$ is a set $S$ of vertices of
$G$ such that every vertex is adjacent to at least one vertex in $S$. The total
domatic number of a graph is the maximum number of total dominating sets which
partition the vertex set of $G$. In this paper we would like to characterize
the cubic graphs with total domatic number at least two.
