The self-condensation of cyclopentanone has been studied over calcined and uncalcined TiO.sub.2-ZrO.sub.2. The catalyst properties were examined by XRD, FTIR, SEM, N.sub.2 adsorption-desorption, and pyridine FTIR. Compared with calcined TiO.sub.2-ZrO.sub.2, uncalcined TiO.sub.2-ZrO.sub.2 exhibited superior catalytic performance (94% conversion of cyclopentanone and 86% yield of dimer). This might be because uncalcined TiO.sub.2-ZrO.sub.2 has both Lewis and Brønsted acids, while calcined TiO.sub.2-ZrO.sub.2 only contains Lewis acids. Kinetics analysis indicated that C-C coupling was the rate-limiting step on the two catalysts. For uncalcined TiO.sub.2-ZrO.sub.2, the C-C coupling occurred between the two species on the catalyst surface. Through the H bond, the cyclopentanone was firmly adsorbed on the catalyst surface by Brønsted acid sites, then the enol intermediate could attack another cyclopentanone polarized by adjacent Lewis acid sites. As a consequence, the coexistence of Brønsted and Lewis acids in catalysts exhibited enhanced activity in cyclopentanone self-condensation. Graphical