Prediction of the financial difficulties of companies has been dealt with over the last years by scientists and economists worldwide. Several prediction models mostly focused on a particular sector of the national economy, have been created also in Slovakia. The main purpose of this paper is to create new prediction models for small and medium-sized companies in Slovakia, based on real data from the Amadeus database from the years 2016–2018. We created prediction models of financial difficulties of companies for 1 year in advance and also a model for 2 years prediction. These models are based on the combination of two methods, discriminant analysis and logistic regression that belong, among others, to the group of the most commonly used methods to derive prediction models of financial difficulties of the companies. The overall prediction powers of the combined model are 90.6%, 93.8% and 90.4%. The results of this analysis can be used for early prediction of the financial difficulties of the company, that could be very useful for all the stakeholders.