Using an electron microscope, cross-striated fibrils with an axial repeat of about 65 nm were detected in the cell nuclei of rat and calf tissues. The nuclei were purified and processed using a "complete medium" (CM) simulating the composition of salts of the intranuclear medium. These fibrils are not the filaments of the nuclear matrix described in the literature. In particular, they are thicker and not branched. The axial repeat in these fibrils is similar to that in extracellular collagen fibrils. Therefore, in this work, the main efforts were aimed at demonstrating the nuclear origin of the observed fibrils. Their presence in the material of nuclei destroyed by ultrasound, their contact with isolated nucleoli and their presence in residual nuclei are shown on samples prepared for electron microscopy in the form of "whole mounts". The sites of attachment of chromatin and of nuclear matrix network to thick cross-striated fibrils were detected. As axial components of condensed chromosomes, thick cross-striated fibrils are preserved during mitosis. Probably, their contacts with chromatin and with elements of nuclear matrix network are also preserved providing reproduction of the internal structure of the nuclei in daughter cells. It is logical to assume that the cross-striated fibrils perform important functions attributed to the nuclear matrix.