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We investigated the behaviour of colloidal particles suspended in nematic liquid crystals. These colloidal particles interact through elastic deformation of the nematic director field which can result in nontrivial collective behavior, leading to the formation of spatially modulated structures. In this paper, the formation of lattice structures is described both by computer simulations and by analytical theory. Effective interactions of the pairs of spherical macroparticles suspended in nematic liquid crystals have been suggested by many authors. Using these pairwise interactions, spatial structures are obtained by means of dynamic simulations. We have suggested a number of possible structures, which may be formed in multi-macroparticle systems. Regions of temperatures and concentrations are determined in which such a structure might appear.