Studies show that short-term synaptic plasticity plays important roles in neural coding and the normal operation of the synapse. Basket cells in the hippocampus demonstrate this plasticity in the form of synaptic depression, and recent in vivo work indicates that basket cell activities contribute significantly to hippocampal output associated with different behavioural states. Thus it is essential to understand the generation and synchronization of patterns produced by basket cell networks with depression. We study two-cell model inhibitory networks with depression and obtain alternating bursting patterns and synchronous activity occurring between bursts. We describe mechanisms for how these patterns emerge by performing several simulations in the plane of different depression time constants, τD. Such patterns might contribute significantly to various population activites observed in the hippocampus.