Genes for nylon oligomer-degrading enzymes are unique in the sense that the enzymes encoded by them are found not to have any appropriate substrates during most of the period of their evolution. Furthermore, these nylB genes form a family not related to any other known gene families. The base sequences of these genes were examined and a common characteristic was found: a long stretch of sequence without chain-terminating base triplets, defined as a nonstop frame (NSF), is being maintained on the antisense strand. Moreover, a certain coding frame is open for both the sense and the antisense sequences, while the other frames have many stop codons. The probability of the presence of these NSFs on the antisense strand of a gene is very small (0.0001-0.0018). In addition, another gene for nylon oligomer degradation was found to have a NSF on its antisense strand, and this gene is phylogenically independent of the nylB genes. Therefore, the presence of these NSFs is very rare and improbable. Even if the common ancestral gene of the nylB family was originally endowed with a NSF on its antisense strand, the probability of this original NSF persisting in one of its descendants of today is only 0.007. Unless an unknown force was maintaining the NSF, it would have quickly disappeared by random emergences of chain terminators. Therefore, the presence of such rare NSFs on all three antisense strands of the nylB gene family suggests that there is some special mechanism for protecting these NSFs from mutations that generate the stop codons. Such a mechanism may enable NSFs to evolve into new functional genes and hence seems to be a basic mechanism for the birth of new enzymes.