Many researchers use mathematical-engineering methods in different domains of life, and medical research is no exception. One area for application of such methods is to assist people with different forms of disabilities. The methods described in the following text are oriented towards the analysis of disordered children's speech with the diagnosis of Specific Language Impairment (SLI), also named as Developmental Dysphasia (DD), and the analysis of the expressive speech. Both methods make use of Kohonen Self-Organizing Maps (KSOM) or Supervised Self-Organizing Maps (SSOM) for the analysis and the classification of features from utterances of healthy and ill children, or adult speakers for emotions analysis. The possibility of cluster visualisation is used for monitoring of disorder trends and therapy success. These experiments also demonstrate the ability of the KSOM or SSOM to classify emotions.