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High-quality dialogue-summary paired data is expensive to produce and domain-sensitive, making abstractive dialogue summarization a challenging task. In this work, we propose the first unsupervised abstractive dialogue summarization model for tete-a-tetes (SuTaT). Unlike standard text summarization, a dialogue summarization method should consider the multi-speaker scenario where the speakers have different roles, goals, and language styles. In a tete-a-tete, such as a customer-agent conversation, SuTaT aims to summarize for each speaker by modeling the customer utterances and the agent utterances separately while retaining their correlations. SuTaT consists of a conditional generative module and two unsupervised summarization modules. The conditional generative module contains two encoders and two decoders in a variational autoencoder framework where the dependencies between two latent spaces are captured. With the same encoders and decoders, two unsupervised summarization modules equipped with sentence-level self-attention mechanisms generate summaries without using any annotations. Experimental results show that SuTaT is superior on unsupervised dialogue summarization for both automatic and human evaluations, and is capable of dialogue classification and single-turn conversation generation.