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In robotic single-port surgery, it is desirable for a manipulator to exhibit the property of variable stiffness. Small-port incisions may require both high flexibility of the manipulator for safety purposes, as well as high structural stiffness for operational precision and high payload capability. This paper presents a new hyperredundant tubular manipulator with a variable neutral-line mechanisms and adjustable stiffness. A unique asymmetric arrangement of the tendons and the links realizes both articulation of the manipulator and continuous stiffness modulation. This asymmetric motion of the manipulator is compensated by a novel actuation mechanism without affecting its structural stiffness. The paper describes the basic mechanics of the variable neutral-line manipulator, and its stiffness characteristics. Simulation and experimental results verify the performance of the proposed mechanism.