Synchronization processes have been studied within the framework of a model describing the dynamics of two inferior olive cells coupled electrotonically through gap junctions surrounded by synaptic inhibitory terminals that block these couplings. A simple model of a chemical synaptic terminal based on the first-order kinetics has been constructed to describe the coupling break. It was found that different types of synchronous behavior exist in the system, depending on the parameters. These are 1:1 and 1:2 synchronization regimes, spike time binding, and others. It was demonstrated that even small changes in the coupling parameters (coupling strength and coupling break delay) may significantly affect the synchronous regimes of interacting cells. In some cases, the activity of one of inferior olive cells is suppressed due to collective dynamics, whereas the activity of the other cell is conserved.