The main goal of this paper is to give the basis for creating a computer-based clinical decision support (CDS) system for laryngopathies. One of approaches which can be used in the proposed CDS is based on the speech signal analysis using recurrent neural networks (RNNs). RNNs can be used for pattern recognition in time series data due to their ability of memorizing some information from the past. The Elman networks (ENs) are a classical representative of RNNs. To improve learning ability of ENs, we may modify and combine them with another kind of RNNs, namely, with the Jordan networks. The modified Elman-Jordan networks (EJNs) manifest a faster and more exact achievement of the target pattern. Validation experiments were carried out on speech signals of patients from the control group and with two kinds of laryngopathies.