  In this paper, we are concerned with $n$-component Ginzburg-Landau equations
on $\rtwo$.By introducing a diffusion constant for each component, we discuss
that the $n$-component equations are different from $n$-copies of the single
Ginzburg-Landau equations.Then, the results of Brezis-Merle-Riviere for the
single Ginzburg-Landau equation can be nontrivially extended to the
multi-component case.First, we show that if the solutions have their gradients
in $L^2$ space, they are trivial solutions.Second, we prove that if the
potential is square summable, then it has quantized integrals, i.e., there
exists one-to-one correspondence between the possible values of the potential
energy and $\nat^n$.Third, we show that different diffusion coefficients in the
system are important to obtain nontrivial solutions of $n$-component equations.
