This study presents a model for mezoscopic molecular dynamics simulations with objects of different scale and properties e.e. atoms, pseudoatoms, rigid and pseudo-elastic bodies, described by the external coordinates and internal degrees of freedom. The Lagrangian approach is used to derive equations of motion and a quaternion representation is used for the description of the dynamics of rigid and pseudo-elastic molecular elements. Stability of the LQMD algorithm was tested for a 10-base pair deoxynucleotide. The total energy, momentum and angular momentum are conserved for time-steps up to 20 fs.