We examined chemical oscillations in the Belousov-Zhabotinsky (BZ) reaction with spherical ion-exchange resin bends (radius : 0.1-0.4 mm) loaded with a cationic catalyst, ferroin, in which no traveling wave appears and the oscillation is synchronized over individual beads. The period of the oscillation increases with a decrease in the size of the beads. Based on a theoretical consideration of the effect of the diffusion of active species through the surface of the bead reactor into the bulk aqueous solution, the following relationship was deduced : f/[H2SO4](gamma) proportional to (1 - eta/R) where f is the frequency (Hz) of the oscillation, R is the radius (mm) of the beads, [H2SO4] is the concentration (mol/dm(3)) of sulfuric acid, and gamma and eta are constants. This relationship was consistent with experimental results with values of gamma = 1.4 and eta = 7.4 x 10(-4).