  We study synchronization of oscillators that are indirectly coupled through
their interaction with an environment. We give criteria for the stability or
instability of a synchronized oscillation. Using these criteria we investigate
synchronization of systems of oscillators which are weakly coupled, in the
sense that the influence of the oscillators on the environment is weak. We
prove that arbitrarily weak coupling will synchronize the oscillators, provided
that this coupling is of the 'right' sign. We illustrate our general results by
applications to a model of coupled GnRH neuron oscillators proposed by Khadra
and Li, and to indirectly weakly-coupled lambda-omega oscillators
