Superconducting Tunnel Junctions are considered for their use as new nuclear radiation detectors with high energy resolution, for radioastronomy. In fact they have potentiality for 0.05% resolution, more than one order of magnitude better than conventional detectors. The reasons and the advantages of using this tunnel junctions are briefly introduced. A description of the working principle and the basic experimental set up are also outlined. The attention is focused on Nb/AlOx/Nb junction which is presently the state of art of superconductive tunnel junction technology with respect to stability and cyclability. Junctions with high dynamical resistance in the biasing region are in fact necessary to optimize the signal to noise ratio and then improve the high energy resolution. The characterization at low temperatures (down to 1.2 K) of samples fabricated with a special «island» geometry is presented to demonstrate the feasibility of their use because they satisfy the rather stringent quality requirements. Finally, preliminary results concerning the junction responsivity to nuclear radiation at relatively high temperature (T=1.5 K) are reported. Although the obtained resolution of 700 eV with 6 keV X-rays is far from the theoretical limit, better results can be expected working with the devices at lower temperatures and improving the structure configuration.