  A total coloring of a graph $G$ is a coloring of its vertices and edges such
that no adjacent vertices, edges, and no incident vertices and edges obtain the
same color. An \emph{interval total $t$-coloring} of a graph $G$ is a total
coloring of $G$ with colors $1,2,\...,t$ such that at least one vertex or edge
of $G$ is colored by $i$, $i=1,2,\...,t$, and the edges incident to each vertex
$v$ together with $v$ are colored by $d_{G}(v)+1$ consecutive colors, where
$d_{G}(v)$ is the degree of the vertex $v$ in $G$. In this paper we investigate
some properties of interval total colorings. We also determine exact values of
the least and the greatest possible number of colors in such colorings for some
classes of graphs.
