We show that the interlayer tunneling I-V in double-layer quantum Hall stat
es displays a rich behavior which depends on the relative magnitude of samp
le size, voltage length scale, current screening, disorder, and thermal len
gths. For weak tunneling. we predict a negative differential conductance of
a power-law shape crossing over to a sharp zero-bias peak. An in-plane mag
netic field splits this zero-bias peak, leading instead to a "derivative" f
eature at V-B(B-\ \) = 2 pi hvB(\ \)d/e phi (upsilon), which gives a direct
measurement of the dispersion of the Goldstone mode corresponding to the s
pontaneous symmetry breaking of the double-layer Hall state.