The experiments with pulsed muon beam and DC muon beam are in a complementary relationship mutually. At J-PARC, two spectroscopy experiments to study the hyperfine splitting in muonic atoms with high-intensity pulsed muon beam were proposed. A microwave spectroscopy of muonium is in progress and a laser spectroscopy of muonic hydrogen is in preparation. In this talk, status of these two experiments will be reported.