The degree of compaction of the eukaryotic chromatin in vivo and in vitro is highly sensitive to the ionic environment. We address the question of the effect of multivalent ions on the interactions and mutual organization of the chromatin structural units, the nucleosome core particles (NCPs). Conditions of precipitation of NCPs in the presence of 10 mM Tris buffer and various amounts of either magnesium (Mg(2+)) or spermidine (Spd(3+)) are explored, compared, and discussed in relation to theoretical models. In addition, the structure of the aggregates is analyzed by complementary techniques: freeze-fracture electron microscopy, cryoelectron microscopy, and x-ray diffraction. In Mg(2+)-NCP aggregates, NCPs tend to stack on top of one another to form columns that are not long-range organized. In the presence of Spd(3+), NCPs precipitate to form a dense isotropic phase, a disordered phase of columns, a two-dimensional columnar hexagonal phase, or a three-dimensional crystal. The more ordered phases (two-dimensional or three-dimensional hexagonal) are found close to the precipitation line, where the number of positive charges carried by cations is slightly larger than the number of available negative charges of the NCPs. All ordered phases coexist with the dense isotropic phases. Formation of hexagonal and columnar phases is prevented by an excess of polycations.