Nonlinear A.C. impedance measurements were conducted in the 50BiV-50SrBAlO nanocomposite as a function of frequency, temperature and A.C. voltage. This material is ferroelectric below temperature of 730 K, and above 730 K is a good ion-conductor. For this nanocomposite a low A.C. voltage of 1 V-rms, is enough to observe high nonlinearities. The origin of these nonlinear effects depends on the temperature and frequency. In the high temperature and low frequency region, the nonlinearities are due to interfacial processes. In the low temperatures and higher frequencies, the nonlinearities may be also correlated with ion-transport processes: hopping and blocking in glass matrix and phase boundaries. The ferroelectric properties of the Bi2VO5.5 nanocrystallites are also possible origin of nonlinear effects. However, their contribution into nonlinearities is weaker than from the other observed processes. It is shown that a decrease of the Bi2VO5.5 crystallites size from micro- to nanometers and introduction of additional structural disorder into material significantly decrease the real part of the third order electric susceptibility coefficient but does not influence the ratio of the third harmonic to the base conductivity. It is suggested that the ferroelectric nanoregions are single-domain and the nonlinearities derived from domain walls probably are not observed.