  We establish an existence theorem for the doubly periodic vortices in a
generalized self-dual Chern--Simons model. We show that there exists a critical
value of the coupling parameter such that there exits self-dual doubly periodic
vortex solutions for the generalized self-dual Chern--Simons equation if and
only if the coupling parameter is less than or equal to the value. The energy,
magnetic flux, and electric charge associated to the field configurations are
all specifically quantized. By the solutions obtained for this generalized
self-dual Chern--Simons equation we can also construct doubly periodic vortex
solutions to a generalized self-dual Abelian Higgs equation.
