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The ternary T-gate can be used as a basic building block to construct both combinational and sequential circuits. Since the T-gate is one kind of tree-type universal logic module, any combinational circuit can be built up with modular logic arrays. For constructing ternary memory elements, however, the T-gate is required to be static hazard-free. A theoretical study is done on the necessary conditions for the practical realization of the static-hazard-free T-gate. On the basis of the result obtained, the static-hazard-free T-gate is realized using the ECL technique. The static-hazard-free T-gates obtained here can be used as building blocks to construct memory elements. Various memory elements such as D flip-flap-flop (FFF), D master-slave FFF, B master-slave FFF, and counting FFF is constructed easily. Using these memory elements, three different types of ternary counters can be designed and realized. They are an asynchronous signed ternary counter, a synchronous signed ternary counter, and a counter based on a shift register. Their design methods are discussed. These ternary counters are superior to the binary ones in that the up-down cotnting can easily be carried out by one input signal.