Two stages of exploring the lunar surface as a target for the interaction of ultrahigh-energy cosmic rays and neutrinos are discussed. The first step is connected with the Lunar Orbital Radio Detector (LORD) experiment in the space mission Luna-Glob, scheduled for the near future. The current status of the LORD instrument development is represented. The aperture of the lunar orbital radio detector exceeds all existing ground-based detector arrays. Successful completion of the LORD experiment will permit to consider the second step of the program namely multi-satellite lunar systems to increase the statistics and the accuracy of the experiment.