  Nonlinear conductivity effects are studied experimentally and theoretically
for thin samples of disordered ionic conductors. Following previous work in
this field the {\it experimental nonlinear conductivity} of sodium ion
conducting glasses is analyzed in terms of apparent hopping distances. Values
up to 43 \AA are obtained. Due to higher-order harmonic current density
detection, any undesired effects arising from Joule heating can be excluded.
Additionally, the influence of temperature and sample thickness on the
nonlinearity is explored. From the {\it theoretical side} the nonlinear
conductivity in a disordered hopping model is analyzed numerically. For the 1D
case the nonlinearity can be even handled analytically. Surprisingly, for this
model the apparent hopping distance scales with the system size. This result
shows that in general the nonlinear conductivity cannot be interpreted in terms
of apparent hopping distances. Possible extensions of the model are discussed.
