Every logic style has certain advantages for a specific application. Therefore, it is essential to introduce and investigate different logic styles. Differential cascode voltage switch logic (DCVSL) with the inherent redundancy is known to be an ideal logic style for error detection applications. This study combines ternary static DCVSL (SDCVSL) with dynamic logic (DL) to realise ternary dynamic DCVSL (DDCVSL) by means of a single power source. At first, it is shown that why the same static-to-dynamic conversion method in binary logic fails to operate correctly in ternary logic. Then, two solutions are given. Static power dissipation and switching activity are particularly dealt with in the second proposed ternary DDCVSL to reduce power consumption. The new designs are simulated and tested by using HSPICE simulator and 32 nm Stanford carbon nanotube field effect transistor model. Simulation results and comparisons with a vast range of conventional and state-of-the-art competitors show prominence and great potential for the new ternary circuit methodology. For example, the authors second proposed ternary DDCVSL AND/NAND has 19.7, 37.4, and 60.5% higher performance than some famous static ternary logic styles such as CMOS-like, SDCVSL, and pseudo N-type, respectively, in terms of energy consumption.