Interference between one cognitive behavior or sensory stimulus and subsequent behaviors is a commonly observed effect in the study of human cognition and Psychology. Traditional connectionist approaches explain this phenomenon by mutually inhibiting neural populations underlying those behaviors. Here, we present an alternative model, relying on a more detailed use of synaptic dynamics, in which populations of purely excitatory neurons can nonetheless interfere with each other, causing inhibition of activation for a varying amount of time. The fundamental, biologically motivated, mechanism in the model relies on current “spilling over” from an active neural population into another one, thereby depleting the latter population’s synaptic resources. The principles underlying the model may find applications even in the design of problemsolving artificial neural networks.