2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/41214The issue of existence of Majorana neutrinos with masses of the order of TeV and substantial couplings is addressed. A general neutrino mass matrix $M_ν$ with both features is constructed, however, the form of $M_ν$ is constrained very much by severe relations among the elements of $m_D$ and $M_R$ submatrices of $M_ν$. These general relations follow from the perturbative construction of the light neutrino mass spectrum. To avoid such large correlations between low mass parameters in $m_D$ and large mass parameters in $M_R$, the Jeżabek-Sumino see-saw model of bi-maximal neutrino mixing adopted to the TeV scale and the issue of possible symmetries of the matrix $M_ν$ are discussed. Results are supported by a few numerical examples which show directly the complexity of the problem.Added a section on fine-tuning problems and symmetry arguments, abstract, conclusions modified. To appear in Acta Phys. Pol. BHigh Energy Physics - Phenomenologytext