The relationship between the hidden periodicities in DNA sequences and the nucleosome units is investigated. It is shown that in the vicinity of lengths of about 200 bases there are statistically significant periodicities which remain approximately universal for exon-intron sequences both in the different genes and the different eukaryotic species. The additional analysis displays, nevertheless, that these approximately coincident universal periodicities can be generated by a variety of mechanisms. The relevance of the features observed to the structure of chromatin is discussed.