  A set $S$ of vertices of graph $G$ is a \textit{defensive alliance} of $G$ if
for every $v \in S$, it holds $|N[v] \cap S| \geq |N[v]-S|$. An alliance $S$ is
called $global$ if it is also a dominating set. In this paper, we determine the
exact values of the global defensive alliance number of lexicographic products
of path and cycles.
