We study resonant tunnelling through double-barrier structures under a
n applied bias voltage, in which nonlinearities due to self-interactio
n of electrons in the barrier regions are included. As an approximatio
n, we concern ourselves with thin barriers simulated by delta-function
potentials. This approximation allows for an analytical expression of
the transmission probability through the structure. We show that the
typical peaks due to resonant tunneling decrease and broaden as nonlin
earity increases. The main conclusion is that nonlinear effects degrad
e the peak-to-valley ratio but improve the maximum operation frequency
of the resonant tunnelling devices.