Two different adaptive immune systems (AIS) are present in the two phyla of vertebrates (jawed vertebrates and cyclostomes). The jawed vertebrate system is based on IG/TCR/RAG/MHC while the cyclostome system is based on VLRC5 and AID-like enzymes both systems using homologous Cell types (B-cell and B-cell Like, T-cell and T-cell like). We will present our current view of the evolution of these two AISs and present alternative hypotheses that could explain the apparent convergent evolution of the two systems. We will also discuss why comparative immunology analyses should be based on evolutionary biology approaches and not on the scale of progress one.