  We introduce a class of PT-symmetric systems which include mutually matched
nonlinear loss and gain (inother words, a class of PT-invariant Hamiltonians in
which both the harmonic and anharmonic parts are non-Hermitian). For a basic
system in the form of a dimer, symmetric and asymmetric eigenstates, including
multistable ones, are found analytically. We demonstrate that, if coupled to a
linear chain, such a nonlinear PT-symmetric dimer generates new types of
nonlinear resonances, with the completely suppressed or greatly amplified
transmission, as well as a regime similar to the electromagnetically-induced
transparency (EIT). The implementation of the systems is possible in various
media admitting controllable linear and nonlinear amplification of waves.
