Some methods of synthesis of networks composed of ternary majority elements such as the three-stable-state parametron or twin are studied. It is shown that three-place majority operation and diametrical negation (negation in the strong sense) with constants are functionally complete in three-valued logic. Classes of functions of two variables are studied for which networks realizing them contain no more than three cascades. This provides a possibility of realizing these functions in one full time unit in the case of three-cycle excitation. Methods of synthesis are developed for the networks which realize functions of an arbitrary number of variables. These methods are based on the excluding of one or several variables simultaneously. Considerations are proposed on the order of the excluding variables. Methods of majority decomposition of functions of three-valued logic are developed.