This paper proposes a simplified oscillator model, called binary-oscillator , and develops a class of neural network models having binary-oscillators as basic units. The binary-oscillator has a binary dynamic variable v = ±1 modeling the “membrane potential” of a neuron, and due to the presence of a “slow current” (as in a classical relaxation-oscillator) it can oscillate between two states. The purpose of the simplification is to enable abstract algorithmic study on the dynamics of oscillator networks. A binary-oscillator network is formally analogous to a system of stochastic binary spins (atomic magnets) in statistical mechanics.