Development of a mechanism with dual remote center of motion (dual-RCM mechanism) intended for teleoperated ophthalmic surgery is reported in this paper. First, characteristics of RCM mechanisms are analyzed. Then, a method to synthesize dual-RCM mechanisms is proposed. Further the mechanical design parameters are optimized to synthesize types of mechanisms meeting functional requirements as well as workspace constraints. The dual-RCM mechanism intended for teleoperated ophthalmic surgery includes two end-effectors: one provides the tool insertion, the other tracks eye movement. The superiority is embodied in the self-synchronized motion of double end-effectors, which allows RCM point of the working instrument to track the penetration point real-time, thereby enhancing microsurgical accuracy. In the proposed implementation, a conceptual helmet mechanical architecture integrating surgical tools with triple-parallelogram linkages is introduced to release the surgeon's hands by enabling more robotic technologies during the procedures. The vision of the research is to help revolutionize the ophthalmic surgical procedures from bimanual fashion to master-slave teleoperation.