This research reports the results of a study of the global and local chemical reactivity of the peptide hormones Oxytocin and Vasopressin based on the calculation of descriptors coming from Conceptual DFT as well as from Molecular Electron Density Theory for their consideration as a tool to explain the molecular interactions, and as a useful complement to those approximations based on Molecular Docking. The knowledge of the values of the global and local descriptors of the molecular reactivity of the Oxytocin and Vasopressin peptide hormones that have been studied through our proposed methodology could be useful in the development of new drugs based on these compound or some analogs relying in the chemical interaction between these peptides and their biological receptors of protein kind. It can be concluded that both approximations to the local chemical reactivity based on the descriptors are equally valid and complement each other, while the choosing of the Population Analysis used in their calculation is not a crucial point to be considered.