  The paper is concerned with the study of a control system consisting of one
major agent and many identical minor agents in the limit case when the number
of agents tends to infinity. To study the limiting system we use the mean field
approach. We first prove the existence and uniqueness of the motion for such
system consisting of finite dimensional and mean field type subsystems. The
main result of the paper is the stability of the motion w.r.t. perturbations of
dynamics, initial data and controls. To illustrate the general theory, we
examine the Stackelberg game where the leader controls the major agent while
the follower affects the minor agents. Using the general theory, we show the
existence of a solution.
