HB-EGF Shedding inhibitors have been expected to become effective medicines for skin diseases caused by the proliferation of keratinocytes. In order to discover novel HB-EGF shedding inhibitors and clarify their structure-activity relationships, 5,6,7,8-tetrahydronaphthylidine-based hydroxamic acid and 5,6,7,8-tetrahydropyrido[3,4-b]pyrazine-based hydroxamic acids have been synthesized. Among the synthesized compounds, the ethoxyethoxy derivative 3o and the methoxypropoxy derivative 3p exhibited much more potent HB-EGF shedding inhibitory activity than CGS 27023A. The structural modification of 5,6,7,8-tetrahydropyrido[3,4-b]pyrazine-based hydroxamic acids enabled us to establish the following structure-activity relationships; the existence of the hydroxamic acid, the sulfonamide, and the phenyl moieties are crucial for a potent HB-EGF shedding inhibitory activity, and the stereochemistry of the alpha carbon of hydroxamic acid is also important. In addition, from the comparison of their HB-EGF shedding inhibitory activities with their MMPs inhibitory activities, we found that the S1' pocket of the responsible enzyme for HB-EGF shedding is deep unlike that of MMP-1.