We study the asymptotic limit of solutions of the Ginzburg-Landau
equations in two dimensions with or without magnetic field. We first
study the Ginzburg-Landau system with magnetic field describing a
superconductor in an applied magnetic field, in the "London limit" of
a Ginzburg-Landau parameter $\kappa$ tending to $\infty$. We examine
the asymptotic behavior of the "vorticity measures" associated to the
vortices of the solution, and we prove that passing to the limit in
the equations (via the "stress-energy tensor") yields a criticality
condition on the limiting measures. This condition allows us to
describe the possible locations and densities of the vortices. We
establish analogous results for the Ginzburg-Landau equation without
magnetic field.