The measurement of the electron spectrum in beta-decays provides a robust direct determination of the values of neutrino masses. The planned rhenium beta-decay experiment, called the "Microcalorimeter Arrays for a Rhenium Experiment" (MARE), might probe the absolute mass scale of neutrinos with the same sensitivity as the Karlsruhe tritium neutrino mass (KATRIN) experiment, which is expected to collect data in a near future. In this contribution we discuss the spectrum of emitted electrons close to the end point in the case of the first unique forbidden beta-decay of 79Se, 107Pd and 187Re. It is found that the p3/2-wave emission dominates over the s1/2-wave. It is shown that the Kurie plot near the end point is within a good accuracy linear in the limit of massless neutrinos like the Kurie plot of the superallowed beta-decay of 3H.