  Let $\mathfrak{g}$ be a basic simple Lie superalgebra over an algebraically
closed field of characteristic zero, and $\theta$ an involution of
$\mathfrak{g}$ preserving a nondegenerate invariant form. We prove that either
$\theta$ or $\delta\circ\theta$ admits an Iwasawa decomposition, where $\delta$
is the canonical grading automorphism $\delta(x)=(-1)^{\overline{x}}x$. The
proof uses the notion of generalized root systems as developed by Serganova,
and follows from a more general result on centralizers of certain tori coming
from semisimple automorphisms of the Lie superalgebra $\mathfrak{g}$.
