  We introduce a notion of spectral singularity that applies for a general
class of nonlinear Schreodinger operators involving a confined nonlinearity.
The presence of the nonlinearity does not break the parity-reflection symmetry
of spectral singularities but makes them amplitude-dependent. Nonlinear
spectral singularities are, therefore, associated with a resonance effect that
produces amplified waves with a specific amplitude-wavelength profile. We
explore the consequences of this phenomenon for a complex delta-function
potential that is subject to a general confined nonlinearity.
