This work is an attempt to study the structural features and evolution
ary patterns of nucleotide sequences by analyzing their 1- through 4-p
let frequencies and statistical relations between them. We present mat
hematical apparatus for this analysis. In particular, we introduce cri
teria to estimate the degree of homogeneity of L-plet composition in a
given set of sequences and the dependence of the L-plet frequencies o
n the composition of lower orders. We apply these criteria to the stud
y of eubacteria, mitochondria and chloroplasts. We demonstrate that L-
plet frequencies are quite useful for revealing evolutionary relations
hip between DNA sequences and that the non-random distribution is more
typical for doublets than to triplets. Non-randomness of triplet comp
osition is more characteristic to coding than to non-coding regions, w
hile no significant differences in dinucleotide composition can be obs
erved. The obtained results can be used for revealing possible mechani
sms of the codon usage phenomena.