  We consider the effect of disorder on coherent tunneling through two barriers
in series, in the regime of overlapping transmission resonances. We present
analytical calculations (using random-matrix theory) and numerical simulations
(on a lattice) to show that strong mode-mixing in the inter-barrier region
induces mesoscopic fluctuations in the conductance $G$ of universal magnitude
$e^2/h$ for a symmetric junction. For an asymmetric junction, the
root-mean-square fluctuations depend on the ratio $\nu$ of the two tunnel
resistances according to ${rms} G = (4e^2/h)\beta^{-1/2} \nu(1+\nu)^{-2}$,
where $\beta = 1 (2)$ in the presence (absence) of time-reversal symmetry.
