  The unusual non-linear effects in hopping conduction of single-crystal
La_{2}CuO_{4 + \delta} with excess oxygen has been observed. The resistance is
measured as a function of applied voltage U (10^{-3} V - 25 V) in the
temperature range 5 K < T < 300 K. At relatively high voltage (U > 0.1 V) the
conduction of sample investigated corresponds well to Mott's variable-range
hopping (VRH). An unusual conduction behavior is found, however, in low voltage
range (approximately below 0.1 V), where the influence of electric field and
(or) electron heating effect on VRH ought to be neglected. Here we have
observed strong increase in resistance at increasing U at T < 20 K, whereas at
T > 20 K the resistance decreases with increasing U. The magnetoresistance of
the sample below 20 K has been positive at low voltage and negative at high
voltage. The observed non-Ohmic behavior is attributable to inhomogeneity of
the sample, and namely, to the enrichment of sample surface with oxygen during
the course of the heat treatment of the sample in helium and air atmosphere
before measurements. At low enough temperature (below 20 K) the surface layer
with increased oxygen concentration is presumed to consist of disconnected
superconducting regions (with T_{c} about 20 K) in poor-conducting matrix. The
results obtained demonstrate that transport properties of cuprate oxides may be
determined in essential degree by structural or stoichimetric inhomogeneities.
This should be taken into account at evaluation of "quality" of
high-temperature superconductors on the basis of transport properties
measurements.
