This paper defines and exemplifies a new computational abstraction called i-dialogue which aims to model communicative situations such as those where an agent conducts multiple concurrent conversations with other agents. The i-dialogue abstraction is inspired both by the dialogue abstraction proposed by [17] and by the STROBE model [4]. Idialogue models conversations among processes by means of fundamental constructs of applicative/functional languages. (i.e. streams, lazy evaluation and higher order functions). The i-dialogue abstraction is adequate for representing multiagent concurrent asynchronous communication such as it can occur in service providing scenarios on today’s Web or Grid. A Scheme implementation of the i-dialogue abstraction has been developed and is available. 1.