Large Audio-Language Models (LALMs) have recently achieved strong performance across various audio-centric tasks. However, hallucination, where models generate responses that are semantically incorrect or acoustically unsupported, remains largely underexplored in the audio domain. Existing hallucination benchmarks mainly focus on text or vision, while the few audio-oriented studies are limited in scale, modality coverage, and diagnostic depth. We therefore introduce HalluAudio, the first large-scale benchmark for evaluating hallucinations across speech, environmental sound, and music. HalluAudio comprises over 5K human-verified QA pairs and spans diverse task types, including binary judgments, multi-choice reasoning, attribute verification, and open-ended QA. To systematically induce hallucinations, we design adversarial prompts and mixed-audio conditions. Beyond accuracy, our evaluation protocol measures hallucination rate, yes/no bias, error-type analysis, and refusal rate, enabling a fine-grained analysis of LALM failure modes. We benchmark a broad range of open-source and proprietary models, providing the first large-scale comparison across speech, sound, and music. Our results reveal significant deficiencies in acoustic grounding, temporal reasoning, and music attribute understanding, underscoring the need for reliable and robust LALMs.