Mutual excitation between two neurons is generally thought to raise the excitation level of each neuron or, if they are both bursty, to act to synchronize their bursts. If only one is bursty, it can induce synchronized bursts in the other cell. Here we show that two nonbursty cells can be induced to burst in synchrony by mutual excitatory synaptic connections, provided the presynaptic threshold for graded synaptic transmission at each synapse is at a different level. This mechanism may operate in a recently discovered network in the lobster Homarus gammarus. By a duality between presynaptic threshold and injected current, we also show that two identical, nonbursty, mutual excitatory cells could be induced to burst in synchrony by injecting differing amounts of current in the two cells. Finally we show that differential oscillations between two mutual excitatory cells could be stopped by a slow-tailed hyperpolarizing current pulse into one cell or a slow-tailed depolarizing pulse into the other.