Coarse-grained Langevin molecular dynamics computer simulations were conducted for systems that mimic solutions of nucleosome core particles (NCPs). The NCP was modeled as a negatively charged spherical particle representing the complex of DNA and the globular part of the histones combined with attached strings of connected charged beads modeling the histone tails. The size, charge, and distribution of the tails relative to the core were built to match real NCPs. Three models of NCPs were constructed to represent different extents of covalent modification on the histone tails: (nonmodified) recombinant (rNCP), acetylated (aNCP), and acetylated and phosphorylated (paNCP). The simulation cell contained 10 NCPs in a dielectric continuum with explicit mobile counterions and added salt. The NCP-NCP interaction is decisively dependent on the modification state of the histone tails and on salt conditions. Increasing the monovalent salt concentration (KCl) from salt-free to physiological concentration leads to NCP aggregation in solution for rNCP, whereas NCP associates are observed only occasionally in the system of aNCPs. In the presence of divalent salt (Mg(2+)), rNCPs form dense stable aggregates, whereas aNCPs form aggregates less frequently. Aggregates are formed via histone-tail bridging and accumulation of counterions in the regions of NCP-NCP contacts. The paNCPs do not show NCP-NCP interaction upon addition of KCl or in the presence of Mg(2+). Simulations for systems with a gradual substitution of K(+) for Mg(2+), to mimic the Mg(2+) titration of an NCP solution, were performed. The rNCP system showed stronger aggregation that occurred at lower concentrations of added Mg(2+), compared to the aNCP system. Additional molecular dynamics simulations performed with a single NCP in the simulation cell showed that detachment of the tails from the NCP core was modest under a wide range of salt concentrations. This implies that salt-induced tail dissociation of the histone tails from the globular NCP is not in itself a major factor in NCP-NCP aggregation. The approximation of coarse-graining, with respect to the description of the NCP as a sphere with uniform charge distribution, was tested in control simulations. A more detailed description of the NCP did not change the main features of the results. Overall, the results of this work are in agreement with experimental data reported for NCP solutions and for chromatin arrays.