  Supercurrent flow is studied in a structure that in the Ginzburg-Landau
regime can be described in terms of an effective double barrier potential. In
the limit of strongly reflecting barriers, the passage of Cooper pairs through
such a structure may be viewed as a realization of resonant tunneling with a
rigid wave function. For interbarrier distances smaller than $d_0=\pi\xi(T)$ no
current-carrying solutions exist. For distances between $d_0$ and $2d_0$, four
solutions exist. The two symmetric solutions obey a current-phase relation of
$\sin(\Delta\varphi/2)$, while the two asymmetric solutions satisfy
$\Delta\varphi=\pi$ for all allowed values of the current. As the distance
exceeds $nd_0$, a new group of four solutions appears, each contaning $(n-1)$
soliton-type oscillations between the barriers. We prove the inexistence of a
continuous crossover between the physical solutions of the nonlinear
Ginzburg-Landau equation and those of the corresponding linearized
Schr\"odinger equation. We also show that under certain conditions a repulsive
delta function barrier may quantitatively describe a SNS structure. We are thus
able to predict that the critical current of a SNSNS structure vanishes as
$\sqrt{T'_c-T}$, where $T'_c$ is lower than the bulk critical temperature.
