Two coupled polymer gels, showing volume oscillation caused by the Belousov-Zhabotinsky (BZ) reaction, were investigated to understand the system composed of mechanically coupled chemical oscillators. The two gels were connected, with a movable plastic sheet in between and placed Under constant compression. Synchronization between two identical gels occurred in a range of compression ratios. The Phase difference between the two oscillating gels was not zero; instead, they showed alternate swelling-deswelling oscillations. Similar phenomena were also observed with gels of different sizes and natural oscillation periods. The experimental results suggest that a physical Change in one gel can to lead a chemical change in the other and vice versa. These results were qualitatively reproduced by a mathematical model based on coupled chemical oscillators.