Sustainable rail transport is an important aim within European transport policy. One way to achieve this is to open-up the rail passenger market to competition. The White paper 2011 of the European Commission (EC) stated that: a competitive and resource efficient transport system presents the need towards opening domestic rail passenger market to competition, including the mandatory award of public service contracts through competitive tendering as a first initiative within the single European transport area. The open access to competition is realised by two different approaches in many European countries; 1) as a public service provision through public tender and 2) on a commercial basis-though open access. Markets for domestic rail passenger services through public tenders have not been opened in many EU countries. The study looks at the rail passenger transport market situation in selected European countries (Austria, Italy, Hungary, Germany, etc.) and places a particular focus on the transport market situation in Slovak Republic. It describes different mechanisms to realise public tenders for the operation of rail passenger transport services under Public Service Obligation (PSO), analysis process of public tenders in the Slovak Republic, quantifies the risk of unsuccessful public tenders and suggest the criteria to achieve successful public tenders for providing rail passenger transport services under PSO.