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The Turing test examines whether AIs exhibit human-like behaviour in natural language conversations. The traditional setting limits each participant to one message at a time and requires constant human participation. This fails to reflect a natural conversational style and hinders the evaluation of dialogue agents based on Large Language Models (LLMs) in complex and prolonged interactions. This paper proposes X-Turing, which enhances the original test with a burst dialogue pattern, allowing more dynamic exchanges using consecutive messages. It further reduces human workload by iteratively generating dialogues that simulate the long-term interaction between the agent and a human to compose the majority of the test process. With the pseudo-dialogue history, the agent then engages in a shorter dialogue with a real human, which is paired with a human-human conversation on the same topic to be judged using questionnaires. We introduce the X-Turn Pass-Rate metric to assess the human likeness of LLMs across varying durations. While LLMs like GPT-4 initially perform well, achieving pass rates of 51.9% and 38.9% during 3 turns and 10 turns of dialogues respectively, their performance drops as the dialogue progresses, which underscores the difficulty in maintaining consistency in the long term.