У дослідженні розглянуто й обґрунтовано теоретичні та методичні основи професійної підготовки майбутніх фахівців залізничного транспорту в системі «коледж-університет». Представлено характеристику неперервної професійної освіти та проаналізовано особливості професійної підготовки майбутніх фахівців залізничного транспорту в умовах неперервної ступеневої освіти. Визначено структуру готовності майбутніх фахівців залізничного транспорту до професійної діяльності, яка охоплює ціннісно-мотиваційний, когнітивний, операційно-діяльнісний і рефлексивний компоненти, передбачає конкретні критерії та показники за чотирма рівнями (низький, середній, достатній і високий). Розроблено концепцію, обґрунтовано і експериментально перевірено педагогічну систему професійної підготовки майбутніх фахівців залізничного транспорту в неперервній освіті, вказано методологічні підходи, інноваційні принципи її дієвості. Виокремлено педагогічні умови, які мають вагомий вплив на вдосконалення професійної підготовки майбутніх фахівців залізничного транспорту в системі неперервної освіти. Запропоновано структурно-функціональну модель педагогічної системи, яка має блочну структуру (цільовий, змістовий, операційний, результативний), і укладено навчально-методичне забезпечення реалізації неперервної підготовки майбутніх фахівців залізничного транспорту під час вивчення дисциплін математичного циклу.^UThe study considers and substantiates the theoretical and methodological foundations of professional education of future railway transport specialists while studying in the system «college–university». As a result of the scientific research, the characteristics of lifelong professional education are presented and the analysis of the peculiarities of professional learning of future railway transport specialists under conditions of lifelong higher education is carried out. It was found out that the state of railway transport development is directly dependent on two factors: human (qualified specialists); technical (modern logistics). The peculiarities of professional education of future railway transport specialists are singled out, which provide: taking into account the content specifics of professional education; integrative approach to general and special training; taking into account the international nature of the industry; the training specifics of humanitarian and technical elite in the field of railway transport; specification and adjustment of general and special learning goals; development and implementation of special courses of professional disciplines on key issues of railway transport and general problems of the industry; orientation on current state and prognostic directions of railway transport development in the context of economic and social integration world trends; development of specific ways to modernize the learning process.During research an analysis of education quality was conducted as an important component of professional education of future railway transport specialists. It is established that the purpose of professional education of railway transport specialists is to train employees who will be competitive in the labor market of transport infrastructure, management, as well as to promote national, cultural and universal values, a stable life position on «lifelong learning»; combination of professional education with natural inclinations and abilities; formation of general and special competencies.Analysis of professional education quality of students in the system «college– university» should be carried out at the following levels: epistemological (at the level of categories); empirical (reflection of thought processes in practice); scientific and theoretical (reflection of the science peculiarities). In the methodological plane of designing high-quality professional education of future railway transport specialists in the system «college–university» should cover the following characteristics: content, purpose, methods of educational process; technologies, forms of educational process organization; subject-subject and subject-object relations in the educational process; linear and nonlinear connections in the middle of the educational system. Practically, the quality of professional education is characterized from the following positions: expediency (compliance with the demands of society and the individual); comparability (of various educational programs; their compatibility); clarity (both the learning process and the result; transparency of the system); mobility (flexibility - to respond quickly to the demands of time); competitiveness (graduates in the labor market of both national and international importance).In order to study the quality of future specialists' professional education in a particular institution, it is necessary to organize monitoring, which aims to perform specific functions: ascertaining (study of student's achievement quality in a particular discipline; study of graduates' employment, etc.); controlling (determining the compliance of the provided educational services provided by the Educational Standards that meet each qualification level); strategic (study of the external and internal factors effects on the quality of education; strategic transformations in the education system in order to bring the latter to a level that can better meet the needs of today, etc.).The concept is developed, pedagogical system of professional education of future railway transport specialists in lifelong education is substantiated and experimentally checked, methodological approaches, innovative principles of its efficiency are defined. The pedagogical conditions that have significant influence on improving education of future railway transport specialists in the system of lifelong education are highlighted. The structural and functional model of the system, which has a block structure (purposeful, informatory, operational, effective) is presented and the educational and methodical support of lifelong education realization of future railway transport specialists during studying disciplines of a mathematical cycle is offered.