  If $G$ is a group of permutations of a set $\Omega$ and $\alpha \in \Omega$,
then the {\em $\alpha$-suborbits} of $G$ are the orbits of the stabilizer
$G_\alpha$ on $\Omega$. The cardinality of an $\alpha$-suborbit is called a
{\em subdegree} of $G$. If the only $G$-invariant equivalence classes on
$\Omega$ are the trivial and universal relations, then $G$ is said to be a {\em
primitive} group of permutations of $\Omega$.
  In this paper we determine the structure of all primitive permutation groups
whose subdegrees are bounded above by a finite cardinal number.
