An azabicyclo compound (I) or a salt thereof in accordance with the present invention has an excellent inhibiting action on matrix metalloproteases (MMPs) activity, and is useful for pharmaceutical, cosmetic and skin external compositions. ##STR00001## wherein R is H, alkyl, heteroalkyl, aryl, heteroaryl, arylalkyl, heteroarylalkyl, acyl, COOR.sup.1, carbamoyl or SO.sub.2R.sup.2 (wherein R.sup.1 and R.sup.2 each are alkyl, heteroalkyl, aryl, heteroaryl, arylalkyl or heteroarylalkyl); X is methylene, ethylene or propylene; and ##STR00002## is a single bond or a double bond.