This invention pertains to certain active carbamic acid compounds which inhibit HDAC activity and which have the following formula: (1) A is an aryl group; Q.sup.1 is a covalent bond or an aryl leader group; J is a sulfonamide linkage selected from: --S(.dbd.O).sub.2NR.sup.1-- and --NR.sup.1S(.dbd.O).sub.2--; R.sup.1 is a sulfonamido substituent; and, Q.sup.2 is an acid leader group; with the proviso that if J is --S(.dbd.O).sub.2NR.sup.1--, then Q.sup.1 is an aryl leader group; and pharmaceutically acceptable salts, solvates, amides, esters, ethers, chemically protected forms, and prodrugs thereof. The present invention also pertains to pharmaceutical compositions comprising such compounds, and the use of such compounds and compositions, both in vitro and in vivo, to inhibit HDAC, and, e.g., to inhibit proliferative conditions, such as cancer and psoriasis.