  A new form to construct complex superpotentials that produce real energy
spectra in supersymmetric quantum mechanics is presented. This is based on the
relation between the nonlinear Ermakov equation and a second order differential
equation of the Schroedinger type. The superpotentials so constructed are
characterized by the Ermakov parameters in such a way that they are always
complex-valued and lead to non-Hermitian Hamiltonians with real spectra, whose
eigenfunctions form a bi-orthogonal system. As applications we present new
complex supersymmetric partners of the free particle that are PT-symmetric and
can be either periodic or regular (of the Poeschl-Teller form). A new family of
complex oscillators with real frequencies that have the energies of the
harmonic oscillator plus an additional real eigenvalue is introduced.
