  Let $G$ be a complex connected reductive algebraic group and $G/B$ denote the
flag variety of $G$. A $G$-homogeneous space $G/H$ is said to be {\it
spherical} if $H$ acts on $G/B$ with finitely many orbits. A class of spherical
homogeneous spaces containing the tori, the complete homogeneous spaces and the
group $G$ (viewed as a $G\times G$-homogeneous space) has particularly nice
proterties. Namely, the pair $(G,H)$ is called a {\it spherical pair of minimal
rank} if there exists $x$ in $G/B$ such that the orbit $H.x$ of $x$ by $H$ is
open in $G/B$ and the stabilizer $H_x$ of $x$ in $H$ contains a maximal torus
of $H$. In this article, we study and classify the spherical pairs of minimal
rank.
