Maximum likelihood estimates of codon and base frequencies from observed amino acid composition of proteins were obtained based on models capable of revealing dependency between base arrangements in the three positions of a codon. Results showed that many of the proteins analysed revealed dependency between base arrangements in the first and second codon positions (first-order interaction). Also, in a number of proteins the interactions between base arrangements seemed to involve simultaneously more than one first order interaction and/or a second-order interaction (among base arrangements in the three codon positions). It was of interest to observe that the model of random base arrangements did not fit the observed amino acid data in almost all of the proteins that were analysed. More than ten amino acids contributed to this deviation from randomness.