The realisation of Delay-Insensitive (DI) asynchronous circuits with a CMOS ternary logic is described in this paper. The main advantage of ternary logic is the easy realisation of a handshake protocol that significantly reduces the communication requirement, one of the major drawback of asynchronous logic. It is shown how general purpose delay-insensitive circuits are designed with standard ternary logic elements and an original completion detection circuit called watchful. Some elemental circuits (shift-register and adder) are designed and simulated and their performance is compared with other asynchronous solutions, showing that a better performance in term of power consumption has been achieved.