Embodiments are provided for adding a token jump logic to an asynchronous processor with token passing. The token jump logic allows token forward jumps and token backward jumps over a cascade of token processing logics in the processor. An embodiment method includes determining, using a token jump logic coupled to a cascade of token processing logics, whether to administer a token forward jump or a token backward jump of a token signal passing through the token processing logics. The token forward jump and token backward jump allow the token signal to skip one or more token processing logics in the cascade. The method further includes monitoring, for each of the token processing logics, a polarity status of a token sense logic, and inverting the polarity status according to the determination at the token jump logic.