Double-beam model is considered in many investigations both theoretical and typically engineering ones. One can find different studies concerning analysis of such structures behaviour, especially in the cases where the system is subjected to dynamic excitations. This kind of model is successfully considered as a reliable representation of railway track. Inclusion of nonlinear physical and geometrical properties of rail track components has been justified by various computational studies and theoretical analyses. In order to properly describe behaviour of real structures their nonlinear properties cannot be omitted. Therefore a necessity to search appropriate analytical nonlinear models is recognized and highlighted in published literature. This paper presents essential extension of previously carried out double-beam system analysis. Two nonlinear factors are taken into account and parametrical analysis of the semi-analytical solution is undertaken with special emphasis on different range of parameters describing nonlinear stiffness of foundation and layer between beams. This study is extended by preliminary discussion regarding the dynamic effects produced by a series of loads moving along the upper beam. A new solution for the case of several forces acting on the upper beam with different frequencies of their variations in time is presented and briefly discussed.