A process for preparing a cyclic ester or a cyclic amide includes contacting hydroxycarboxylic acid and/or amino-carboxylic acid, an ester thereof, or a salt thereof, with acidic zeolite. The hydroxycarboxylic acid is a 2- or 6-hydroxycarboxylic acid, and the amino carboxylic acid is a 2- or 6-amino-carboxylic acid. The zeolite may include two or three interconnected and non-parallel channel systems, in which a channel system includes 10- or more-membered ring channels, and in which a framework Si/X2 ratio is at least 24 as measured by NMR. X is Al or B. The zeolite may include three interconnected and non-parallel channel systems, in which at least two channel systems include 10- or more-membered ring channels, and in which a framework Si/X2 ratio is at least 6 as measured by NMR. The process may be performed at a pressure between 0.5 and 20 bar.