The present invention relates to a novel class of hydroxamic acid derivatives having at least two aryl containing groups, at least one of which is a quinolinyl, isoquinolinyl or benzyl moiety, linked to the hydroxamic acid group through a methylene chain. The hydroxamic acid compounds can be used to treat cancer, for example, brain cancer. The hydroxamic acid compounds can also inhibit histone deacetylase and are suitable for use in selectively inducing terminal differentiation, and arresting cell growth and/or apoptosis of neoplastic cells, thereby inhibiting proliferation of such cells. Thus, the compounds of the present are useful in treating a patient having a tumor characterized by proliferation of neoplastic cells. The compounds of the invention are also useful in the prevention and treatment of TRX-mediated diseases, such as autoimmune, allergic and inflammatory diseases, and in the prevention and/or treatment of diseases of the central nervous system (CNS), such as neurodegenerative diseases.