  We extend the standard intertwining relations used in Supersymmetrical (SUSY)
Quantum Mechanics which involve real superpotentials to complex
superpotentials. This allows to deal with a large class of non-hermitean
Hamiltonians and to study in general the isospectrality between complex
potentials. In very specific cases we can construct in a natural way
"quasi-complex" potentials which we define as complex potentials having a
global property such as to lead to a Hamiltonian with real spectrum. We also
obtained a class of complex transparent potentials whose Hamiltonian can be
intertwined to a free Hamiltonian. We provide a variety of examples both for
the radial problem (half axis) and for the standard one-dimensional problem
(the whole axis), including remarks concerning scattering problems.
