  A subset $S$ of vertices in a graph $G$ is a secure total dominating set of
$G$ if $S$ is a total dominating set of $G$ and, for each vertex $u \not\in S$,
there is a vertex $v \in S$ such that $uv$ is an edge and $(S \setminus \{v\})
\cup \{u\}$ is also a total dominating set of $G$. We show that if $G$ is a
maximal outerplanar graph of order $n$, then $G$ has a total secure dominating
set of size at most $\lfloor 2n/3 \rfloor$. Moreover, if an outerplanar graph
$G$ of order $n$, then each secure total dominating set has at least $\lceil
(n+2)/3 \rceil$ vertices. We show that these bounds are best possible.
