Homologies between tRNAs and rRNAs are identified in searches using various combinations of Escherichia coli, yeast, Halobacterium volcanii and bovine mitochondrial sequences. As in previously reported comparisons, the homologies are too frequent and long to be attributed to coincidence, and similar frequencies from inter- and intraspecies comparisons preclude evolutionary convergence as an explanation. In contrast to the earlier studies, patterns in the positioning of the homologies are now described. Graphing the positions of the homologies along orthogonal axes that represent numbers of bases in tRNA and rRNA shows recurring patterns in the alignments. Preferred spacings of integral multiples of 9 bases are found, suggesting a periodicity in the ancestral structure from which the tRNAs and rRNAs were derived. The periodicity also suggests persistence of a modular format in both classes of molecules that survived changes in sequence that occurred during evolution. A model is proposed for the generation of the ancestral molecule and the early evolution of the coding mechanism. Elongation by self-priming and self-templating gave a hairpin with a 9 base stem. Two additional cycles gave a 70-80 base tRNA-like structure. Additional cycles yielded a tandem repeat of this unit, roughly equivalent in size to the combined rRNAs of prokaryotes. The larger RNA would contain the information and materials for generating the smaller RNAs. It is proposed that multiple recombination among such molecules gave composite structures, presumed progenitors of today's t- and rRNAs. The distribution of the conserved domains among today's species argues for the existence of the ancestral molecule prior to divergence of lines leading to the various kingdoms. Their presence in the different nucleic acids suggests the existence of a nucleic acid with multiple functions prior to partitioning of these functions among the nucleic acids that exist today. The occurrence of overlaps, overlays and consensus alignments among the homologies provides the means for identifying contiguous and neighboring conserved regions and holds promise for the reconstruction of the sequence of an ancestral molecule.