Robust representations of sounds with a complex spectrotemporal structure are thought to emerge in hierarchically organized auditory cortex, but the computational advantage of this hierarchy remains unknown. Here, we used computational models to study how such hierarchical structures affect temporal binding in neural networks. We equipped individual units in different types of feedforward networks with local memory mechanisms storing recent inputs and observed how this affected the ability of the networks to process stimuli context dependently. Our findings illustrate that these local memories stack up in hierarchical structures and hence allow network units to exhibit selectivity to spectral sequences longer than the time spans of the local memories. We also illustrate that short-term synaptic plasticity is a potential local memory mechanism within the auditory cortex, and we show that it can bring robustness to context dependence against variation in the temporal rate of stimuli, while introducing nonlinearities to response profiles that are not well captured by standard linear spectrotemporal receptive field models. The results therefore indicate that short-term synaptic plasticity might provide hierarchically structured auditory cortex with computational capabilities important for robust representations of spectrotemporal patterns.