We investigate the dynamics of a recurrent network of coupled heterogeneous neural oscillators with experimentally observed spike-timing-dependent synaptic plasticity. We show both theoretically and by computer simulations that, in a regime of a balance between synaptic potentiation and depression, the network of such oscillators converges to a stable synchronous state. The stability of this state is fostered by flexible synaptic weights which adjust themselves based on the relative timing of firing of pre- and postsynaptic oscillators.