ABSTRACT: We derived chemical abundances for C, N, O, Na, Mg, and Al in 20 asymptotic giant branch (AGB) stars in the globular cluster (GC) NGC 6752. All these elements (but Mg) show intrinsic star-to-star variations and statistically significant correlations or anticorrelations analogous to those commonly observed in red giant stars of GCs hosting multiple populations. This demonstrates that, at odds with previous findings, both first- and second-generation (SG) stars populate the AGB of NGC 6752. The comparison with the Na abundances of red giant branch stars in the same cluster reveals that SG stars (with mild Na and He enrichment) do reach the AGB phase. The only objects that are not observed along the AGB of NGC 6752 are stars with extreme Na enhancement. This is also consistent with standard stellar evolution models, showing that highly Na and He enriched stars populate the bluest portion of the horizontal branch and, because of their low stellar masses, evolve directly to the white dwarf cooling sequence, skipping the AGB phase.