  A class of one-dimensional lattice models with incommensurate complex
potential $V(\theta)=2[\lambda_r cos(\theta)+i \lambda_i sin(\theta)]$ is found
to exhibit localization transition at $|\lambda_r|+|\lambda_i|=1$. This
transition from extended to localized states manifests in the behavior of the
complex eigenspectum. In the extended phase, states with real eigenenergies
have finite measure and this measure goes to zero in the localized phase.
Furthermore, all extended states exhibit real spectrum provided $|\lambda_r|
\ge |\lambda_i|$. Another novel feature of the system is the fact that the
imaginary part of the spectrum is sensitive to the boundary conditions {\it
only at the onset to localization}.
