This paper analyzes two-handed grasping of a rigid object in the two-dimensional (2-D) space. The two hands under consideration have two fingers, and each finger is equipped with a tactile sensor. The hands are assumed to be respectively installed on two robotic manipulators capable of motion and force control. In a separate paper [1], a necessary condition for proper grasping configurations of two two-fingered hands are obtained. A proper grasping configuration is a configuration of the two hands at the initial contact with the object guaranteeing that a stable grasp can be achieved. A detailed study of the properties of contacts with the two fingers of a hand, and a method to determine if a proper grasping configuration has been reached by the two hands, are provided.