We address the problem of speech act recognition (SAR) in asynchronous conversations (e.g., forums, emails). However, unlike synchronous conversations (e.g., meetings, phone), asynchronous domains lack large labeled datasets to train an effective SAR model. In this paper, we propose methods to effectively leverage abundant unlabeled conversational data and the available labeled data from synchronous domains. We carry out our research in three main steps. First, we introduce a neural architecture based on hierarchical LSTMs and conditional random fields (CRF) for SAR in asynchronous conversations, and show that our method outperforms existing methods when trained on in-domain data only. Second, we improve our initial SAR models by semi-supervised learning in the form of pretrained word embeddings learned from a large unlabeled conversational corpus. Finally, we employ adversarial training to improve the results further by leveraging the labeled data from synchronous domains and by explicitly modeling the shift in two domains.