  A defensive $k$-alliance in a graph is a set $S$ of vertices with the
property that every vertex in $S$ has at least $k$ more neighbors in $S$ than
it has outside of $S$. A defensive $k$-alliance $S$ is called global if it
forms a dominating set. In this paper we study the problem of partitioning the
vertex set of a graph into (global) defensive $k$-alliances. The (global)
defensive $k$-alliance partition number of a graph $\Gamma=(V,E)$,
($\psi_{k}^{gd}(\Gamma)$) $\psi_k^{d}(\Gamma)$, is defined to be the maximum
number of sets in a partition of $V$ such that each set is a (global) defensive
$k$-alliance. We obtain tight bounds on $\psi_k^{d}(\Gamma)$ and
$\psi_{k}^{gd}(\Gamma)$ in terms of several parameters of the graph including
the order, size, maximum and minimum degree, the algebraic connectivity and the
isoperimetric number. Moreover, we study the close relationships that exist
among partitions of $\Gamma_1\times \Gamma_2$ into (global) defensive
$(k_1+k_2)$-alliances and partitions of $\Gamma_i$ into (global) defensive
$k_i$-alliances, $i\in \{1,2\}$.
