The speech transmission via IP networks represents a kind of challenge for today's communications. From the time of traditional PSTN systems the speech transmission has reached a completely new dimension through VoIP. Besides the telecommunication technologies there are other technologies as well as their characteristic aspects that are interlacing here. It is mainly corresponding to signalling methods, speech as an audio signal processing, security and economical aspects of using VoIP. Finally, special care is given to the quality of service delivery as a basic requirement on VoIP systems. Benefits of using VoIP technology are presented generally. Besides all of these factors important for establishing a modern VoIP system this thesis is primarily describing the establishment and the measurement of the audio service quality in IP networks. For that purpose, chapter with measurements of audio service with emphasis on objective measurement of the speech quality is particularly elaborated. As an illustration, there is an example of measurements characteristic for an air traffic management VoIP system presented here. Additionally, there are some measurement simulations made in the laboratory for three different audio codecs in order to show some results of the different network parameters affecting the speech quality transmission.