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This paper explores the capability of Mamba, a recently proposed architecture based on state space models (SSMs), as a competitive alternative to Transformer-based models. In the speech domain, well-designed Transformer-based models, such as the Conformer and E-Branchformer, have become the de facto standards. Extensive evaluations have demonstrated the effectiveness of these Transformer-based models across a wide range of speech tasks. In contrast, the evaluation of SSMs has been limited to a few tasks, such as automatic speech recognition (ASR) and speech synthesis. In this paper, we compared Mamba with state-of-the-art Transformer variants in various speech applications, including ASR, text-to-speech, spoken language understanding, and speech summarization. Experimental evaluations revealed that Mamba achieves comparable or better performance than Transformer-based models, and demonstrated its efficiency in long-form speech processing.