  In this paper we deal with the calculation of the signed (total) Roman
domination numbers, $\gamma_{sR}$ and $\gamma_{stR}$ respectively, on a few
classes of planar graphs from the literature. We give proofs for the exact
values of the numbers $\gamma_{sR}(A_n)$ and $\gamma_{sR}(R_n)$ as well as the
numbers
  $\gamma_{stR}(S_n)$ and $\gamma_{stR}(T_n)$. For some other classes of planar
graphs, such as $Q_n$, %$S_n"$ and $T_n"$, lower and upper bounds on
$\gamma_{sR}$ are calculated and proved. %We give some open problems on the
exact values of $\gamma_{sR}$ and $\gamma_{stR}$ for some classes of planar
graphs.
