Despite the availability of a rapidly growing ribosomal RNA database that now includes organisms in all three primary lines of descent (eubacteria, archaebacteria, and eukaryotes), theoretical treatment of the evolution of the ribosomal RNAs has lagged behind that of the protein genes. In this paper a theory is developed that applies current views of protein gene evolution to the ribosomal RNAs. The major topics addressed are the variability in size, gene arrangement, and processing of the rRNAs among the three primary lines of descent. Among the conclusions are that the rRNAs of eukaryotes retain some primitive features that were probably present in the rRNAs of the earliest cell (the progenote) and that the genes coding for the three major rRNA species were probably originally unlinked.