Agents built on large language models (LLMs) have excelled in turn-by-turn human-AI collaboration but struggle with simultaneous tasks requiring real-time interaction. Latency issues and the challenge of inferring variable human strategies hinder their ability to make autonomous decisions without explicit instructions. Through experiments with current independent *System 1* and *System 2* methods, we validate the necessity of using Dual Process Theory (DPT) in real-time tasks. We propose DPT-Agent, a novel language agent framework that integrates *System 1* and *System 2* for efficient real-time simultaneous human-AI collaboration. DPT-Agent’s *System 1* uses a Finite-state Machine (FSM) and code-as-policy for fast, intuitive, and controllable decision-making. DPT-Agent’s *System 2* integrates Theory of Mind (ToM) and asynchronous reflection to infer human intentions and perform reasoning-based autonomous decisions. We demonstrate the effectiveness of DPT-Agent through further experiments with rule-based agents and human collaborators, showing significant improvements over mainstream LLM-based frameworks. To the best of our knowledge, DPT-Agent is the first language agent framework that achieves successful real-time simultaneous human-AI collaboration autonomously. Code of DPT-Agent can be found in https://github.com/sjtu-marl/DPT-Agent.