Promoting rail transport is one of the effective ways of fighting climate change and reducing the carbon footprint. This has naturally given rise to recent demands on rail transport to increase track capacity by increasing travel speed, number of trains and axle loads. Track design usually considers a critical velocity of the moving force, which is equal to the lowest velocity of wave propagation in the supporting structure, resulting from the dynamic interaction of all parts involved. However, for the above reason, the problem of instability becomes more important. This problem was usually overcome in the past because a single moving mass can only achieve unstable behaviour in the supercritical velocity region, which is already excluded in the design. However, the dynamic interaction of two moving proximate masses can lead to a different situation, which surprisingly worsens with increased damping. Such cases have already been identified in the author’s previous works, however, the fact that such masses should be connected by a rigid bogie may once again shed new light on the problem. In this talk, the conditions for unstable cases in the subcritical range of velocities of two moving proximate masses are summarized and compared with the cases of two-axle bogies. A new method developed by the author is used to solve these problems and the results are presented in dimensionless parameters to cover a wide range of possible scenarios.