Large Audio-Language Models (LALMs) have unclocked audio dialogue capabilities, where audio dialogues are a direct exchange of spoken language between LALMs and humans. Recent advances, such as GPT-4o, have enabled LALMs in back-and-forth audio dialogues with humans. This progression not only underscores the potential of LALMs but also broadens their applicability across a wide range of practical scenarios supported by audio dialogues. However, given these advancements, a comprehensive benchmark to evaluate the performance of LALMs in the open-ended audio dialogue understanding remains absent currently. To address this gap, we propose an Audio Dialogue Understanding Benchmark (ADU-Bench), which consists of 4 benchmark datasets. They assess the open-ended audio dialogue ability for LALMs in 3 general scenarios, 12 skills, 9 multilingual languages, and 4 categories of ambiguity handling. Notably, we firstly propose the evaluation of ambiguity handling in audio dialogues that expresses different intentions beyond the same literal meaning of sentences, e.g., "Really!?" with different intonations. In summary, ADU-Bench includes over 20,000 open-ended audio dialogues for the assessment of LALMs. Through extensive experiments conducted on 13 LALMs, our analysis reveals that there is still considerable room for improvement in the audio dialogue understanding abilities of existing LALMs. In particular, they struggle with mathematical symbols and formulas, understanding human behavior such as roleplay, comprehending multiple languages, and handling audio dialogue ambiguities from different phonetic elements, such as intonations, pause positions, and homophones.