Fast development of the x-ray facilities and experimental techniques allows studying the x-ray induced dynamics of complex molecules with ultra-high temporal and spatial resolution using advanced x-ray spectroscopy methods. Growing experimental interest requires already now theoretical simulations on a high accuracy level in order to model complex nonlinear x-ray processes for XFEL applications. Theoretical background for x-ray non-linear processes and pump-probe spectroscopy techniques was initially developed in our group and applied to studies of atoms and molecules. In the present project we plan to take an advantage of high performance computers at SNIC in order to make a qualitative jump to highly accurate simulations of the electron-nuclear dynamics of polyatomic systems in XFEL pulses taking into account the nonlinear interaction with strong x-ray radiation. The numerical simulations proposed in the project are based on semi-classical approach when propagation of the x-ray pulses is described by classical electrodynamics (Maxwell equations) while the material response is treated on quantum mechanical level employing the density matrix equations. Sufficient part of the project is devoted to fully quantum mechanical modelling of the nuclear wave packet dynamics in multidimensional space. In the present project we plan to use a well optimized home-made codes eSPec, XRAMP and RAM developed for the solution of the complex dynamical problems on x-ray transitions. The software was tested on multi-core clusters and successfully applied for studies of small molecular systems. One of the main goals of the project is to support the experimental activities of our collaborators from x-ray facilities MAX IV (Lund, Sweden) and The European XFEL and FLASH II (Hamburg, Germany). Our calculations performed during the last 12 month (project 2016/1-77) resulted in five papers published in high-level scientific journals [Faraday Discussions, DOI: 10.1039/c6fd00103c; Nature Communications, DOI: 10.1038/ncomms14165; Physical Review A, DOI: 10.1103/PhysRevA.93.032510, DOI: 10.1103/PhysRevA.94.063413; Scientific Reports, accepted]. Moreover, in the framework of the project software allowing for 2 and 3 dimensional systems in strong x-rays was developed and tested on SNIC computers, including parallel version. In the present proposal, we will use the software for accurate quantum calculations of the real systems (water, methanol) with practical applications.