Interference between one cognitive behavior or sensory stim-ulus and subsequent behaviors is a commonly observed effect in the study of human cognition and Psychology. Traditional connectionist approaches explain this phenomenon by mutu-ally inhibiting neural populations underlying those behaviors. Here, we present an alternative model, relying on a more de-tailed 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 neu-ral 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 problem-solving artificial neural networks.