The subject of this paper is to research the dynamic and the possibilities of modelling the development of the passenger transport demand in the railway passenger suburban traffic system of the City of Zagreb and the inland railway passenger traffic in the Republic of Croatia. The researched traffic sizes by their characteristics are quantitative indicators of the railway passenger traffic transport demand, stated by the number of transported passengers and realised transport operation within the system. The appropriate mathematical and statistical analysis of passenger transport demand established the existing condition on the level of the traffic system; then, a mathematical and prognostic trend model of the researched size development dynamic was made. The prognostic trend model of the traffic size has been represented by an appropriate equation, with the calculation of the appertaining determination coefficient as a measure of quality, establishing the level of statistical significance of the given data description. Index Terms-railway passenger demand, public urban and suburban passenger transport system, growth, development