Development of interpreting telephony or a speech-to-speech translation system is one of the ultimate goals of speech recognition, natural language processing, artificial intelligence and machine translation. This paper describes DmDialog, a speech-to-speech dialogue translation system. DmDialog is one of the first experimental systems to perform speech-to-speech translation and the first to demonstrate the possibility of simultaneous interpretation. The hybrid parallel system integrates parallel marker-passing and connectionist networks. Other characteristics of the system include a simultaneous interpretation capability, mixed-initiative discourse understanding, cost-based ambiguity resolution and an integration of case-based and constraint-based processing. DmDialog is implemented and has been publicly demonstrated since March 1989. The current implementation translates Japanese into English and operates on the ATR's conference registration domain. Massively parallel implementations have been carried out on various machines and attained high performance.