The oral technologies created a new type of the human-computer interaction. The oral servers and oral portals which implement a new model of human-computer communications may be studied using the methods of the queuing theory. Development of the analytical models to estimate some numerical characteristics of the human-computer one-channel dialogue such as the probability of successful dialogue, number of overinterrogations, and mean time of dialogue are the immediate subject matters of such studies. These characteristics may be used further to analyze operation of the entire queuing system that models the multichannel oral portal. The main parameters of the human-computer dialogue such as the probability of correct recognition of an element and the entire dialogue at overinterrogations and the time used for a dialogue element were considered. The parameters for estimation of the dialogue length were determined. A classification of the dialogue control algorithms at oral interaction of the client with the computer-aided information and servicing systems was developed. The algorithms were compared in terms of duration with regard for the desired reliability of recognition.