The distribution of lambda3883 CN band strengths has been investigated among stars in the asymptotic giant branch phase of evolution in the globular clusters M5 and NGC 6752, as well as among red horizontal branch stars in M4. Differences in the strength of the CN band have been identified among the asymptotic giant branch stars in both M5 and NGC 6752. Synthetic spectrum computations reveal that the differences in the strength of this band between the CN-strongest stars found on the red giant and asymptotic giant branches of M5 can be accounted for entirely by their differences in effective temperature and gravity, without having to invoke differences in the surface abundances of carbon and nitrogen. However, the asymptotic giant branch stars in M5 are observed to show a smaller spread of CN band strengths than red giants of comparable color, and the majority of them appear to be analogs to the CN-strong stars found on the red giant branch. A sample of seven red horizontal branch stars in M4 shows little variation in the strength of the lambda3883 CN band, with only two stars exhibiting possible CN differences from the remainder of the sample. Synthetic spectrum calculations indicate that the majority of the HB stars observed in M4 are counterparts to the CN-strong giants in this cluster. The evolved stars in M4 and M5 are therefore found to be predominantly CN enhanced, whereas such stars appear to be rare on the asymptotic giant branch of NGC 6752. It is suggested that the differences in the CN distributions among the evolved stars in these clusters may be a consequence of their envelopes having been subjected to differing degrees of C --> N processing during the preceding red giant branch phase of evolution.