Video Temporal Grounding (VTG) is a crucial capability for video understanding models and plays a vital role in downstream tasks such as video browsing and editing. To effectively handle various tasks simultaneously and enable zero-shot prediction, there is a growing trend in employing video LLMs for VTG tasks. However, current video LLM-based methods rely exclusively on natural language generation, lacking the ability to model the clear structure inherent in videos, which restricts their effectiveness in tackling VTG tasks. To address this issue, this paper first formally introduces causal event modeling framework, which represents videos as sequences of events, and predict the current event using previous events, video inputs, and textural instructions. Each event consists of three components: timestamps, salient scores, and textual captions. We then propose a novel task-interleaved video LLM called TRACE to effectively implement the causal event modeling framework in practice. The TRACE processes visual frames, timestamps, salient scores, and text as distinct tasks, employing various encoders and decoding heads for each. Task tokens are arranged in an interleaved sequence according to the causal event modeling framework's formulation. Extensive experiments on various VTG tasks and datasets demonstrate the superior performance of TRACE compared to state-of-the-art video LLMs. Our model and code are available at \url{https://github.com/gyxxyg/TRACE}.

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