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Light propagation in optical waveguides with periodically modulated index ofrefraction and alternating gain and loss are investigated for linear andnonlinear systems. Based on a multiscale perturbation analysis, it is shownthat for many non-parity-time ($\mathcal{PT}$) symmetric waveguides, theirlinear spectrum is partially complex, thus light exponentially grows or decaysupon propagation, and this growth or delay is not altered by nonlinearity.However, several classes of non-$\mathcal{PT}$-symmetric waveguides are alsoidentified to possess all-real linear spectrum. In the nonlinear regimelongitudinally periodic and transversely quasi-localized modes are found for$\mathcal{PT}$-symmetric waveguides both above and below phase transition.These nonlinear modes are stable under evolution and can develop from initiallyweak initial conditions.

Light propagation in periodically modulated complex waveguides