This paper presents a practical method for automatic tip-over prevention and path following control of a redundant nonholonomic mobile modular manipulator. According to modular robot concept, the mobile platform is treated as a special module attached to the base of the modular manipulator, then an integrated structure is constructed and its dynamic modeling is performed. A new tip-over stability criterion based on the supporting forces is proposed in consideration of inertia, gravity, and acceleration. An online fuzzy logic (FL) self-motion planner and an adaptive neural-fuzzy controller (ANFC) are presented: The former is used to generate desired self-motions in a real-time manner, and the latter is used to prevent the robot from tipping over and to control the end-effector to follow a desired spacial trajectory at the same time. The proposed algorithm does not need any a priori knowledge of dynamic parameters and can suppress bounded external disturbances effectively. Simulation results for a real robot validate the dynamic modeling method and the controller design algorithm.