Modern methods of speech synthesis are not suitable for restoration of song signals due to lack of vitality and intonation in the resulted sounds. The aim of presented work is to synthesize melismas met in Lithuanian folk songs, by applying Artificial Neural Networks. An analytical survey of rather a widespread literature is presented. First classification and comprehensive discussion of melismas are given. The theory of dynamic systems which will make the basis for studying melismas is presented and finally the relationship for modeling a melisma with nonlinear and dynamic systems is outlined. Investigation of the most widely used Linear Prediction Coding method and possibilities of its improvement. The modification of original Linear Prediction method based on dynamic LPC frame positioning is proposed. On its basis, the new melisma synthesis technique is presented.Developed flexible generalized melisma model, based on two Artificial Neural Networks – a Multilayer Perceptron and Adaline – as well as on two network training algorithms – Levenberg- Marquardt and the Least Squares error minimization – is presented. Moreover, original mathematical models of Fortis, Gruppett, Mordent and Trill are created, fit for synthesizing melismas, and their minimal sizes are proposed. The last chapter concerns experimental investigation, using over 500 melisma records, and corroborates application of the new mathematical models to melisma synthesis of one [ ...].