An experimental setup for studying the reaction d + d → 2He + 2 n is described, and the first preliminary results of measurements at a deuteron energy of 15 MeV are presented. The experiment was aimed at determining the energies of quasibound singlet states of two-nucleon systems (nn and pp), these energies being important features of nucleon–nucleon (NN) interaction. The measurements in question were performed at a deuteron beamfrom the U-120 cyclotron of the Skobeltsyn Institute ofNuclear Physics (Moscow State University). Two protons and one of the neutrons fromthe breakup of the dineutron system were detected in the experiment. A simulation of the reaction in question and preliminary experimental results reveal the possibility of determining the energy of quasibound singlet states on the basis of the form of the energy spectra of particles originating from their breakup.