In this paper the author covers all important speech coding methods which have effected the developing process of speech coding algorithms. The algorithms included, are from basic one to the most sofisticated algorithms, which are part of the modern digital radiocommunication cellular systems. The introductory part, based on the example of a digital radiocommunication system using the TETRA standard, shows the high level of complexity of the system, highlighting problems such as transforming of speech signal into digital form as well as increasing of spectral efficiency. The above mentioned issues could be addresed by using adequate coding methods. This emphasizes the key role of speech coding algorithms in the modern mobile radiocommunication systems. Following the introductory part, the paper offer the analysis and the overview of the basic elements of an algorithm, in order to give more detailed insight into the algorithm coding structure, main functioning principles of an algorithm and the procedures used for development of modern and powerful speech coding algorithms. Speech coding algorithms have been classified according to their main characteristics and techniques used for coding of a speech signal. For a single communication standard the author, using comperative analysis, has defined specific coding procedures that have been choosen based on their main characteristics and elements. Using comperative analysis, the author has defined characteristics and elements crucial in a process of choosing coding algorithm for a specific standard. These elements are also used as the basis for choosing the speech coding algorithms during the developing phase of digital radiocommunication system according to the TETRA standard.