  A Ginzburg-Landau type equation with nonlocal coupling is derived
systematically as a reduced form of a universal class of reaction-diffusion
systems near the Hopf bifurcation point and in the presence of another small
parameter. The reaction-diffusion systems to be reduced are such that the
chemical components constituting local oscillators are non-diffusive or hardly
diffusive, so that the oscillators are almost uncoupled, while there is an
extra diffusive component which introduces effective nonlocal coupling over the
oscillators. Linear stability analysis of the reduced equation about the
uniform oscillation is also carried out. This revealed that new types of
instability which can never arise in the ordinary complex Ginzburg-Landau
equation are possible, and their physical implication is briefly discussed.
