In an article dealing with abdominal development most of the exercises were executed with a physioball (Swiss ball). When using the physioball however you should keep in mind that many muscles contract isometrically merely to maintain your balance. Because of this most exercises are done through a short range of motion. Full range exercises on the ball can be dangerous if you are not able to keep yourself in support and well balanced during execution. Even when you can maintain balance some of the exercises can still be dangerous.
For example, in the supine physioball trunk rotation you are told to “lie face up on the ball with your lower and mid back supported (on the ball), with a weight held in the hands. You should then rotate slowly to the left and right carrying the weight toward the floor without moving your shoulders independent of your torso.” If done in this manner the entire upper body rotates up to 90 degrees to the right and left. If you did this however, you would roll off the ball and probably injury yourself.
See Kinesiology of Exercise for more information on the reverse trunk twist and other abdominal exercises.