GABAergic synapse reversal potential is controlled by the concentration of chloride. This concentration can change significantly during development and as a function of neuronal activity. Thus, GABA inhibition can be hyperpolarizing, shunting, or partially depolarizing. Previous results pinpointed the conditions under which hyperpolarizing inhibition (or depolarizing excitation) can lead to synchrony of neural oscillators. Here we examine the role of the GABAergic reversal potential in generation of synchronous oscillations in circuits of neural oscillators. Using weakly coupled oscillator analysis, we show when shunting and partially depolarizing inhibition can produce synchrony, asynchrony, and coexistence of the two. In particular, we show that this depends critically on such factors as the firing rate, the speed of the synapse, spike frequency adaptation, and, most important, the dynamics of spike generation (type I versus type II). We back up our analysis with simulations of small circuits of conductance-based neurons, as well as large-scale networks of neural oscillators. The simulation results are compatible with the analysis: for example, when bistability is predicted analytically, the large-scale network shows clustered states.