  Motivated by the rich variety of complex periodic and quasi-periodic patterns
found in systems such as two-frequency forced Faraday waves, we study the
interaction of two spatially periodic modes that are nearly resonant. Within
the framework of two coupled one-dimensional Ginzburg-Landau equations we
investigate analytically the stability of the periodic solutions to general
perturbations, including perturbations that do not respect the periodicity of
the pattern, and which may lead to quasi-periodic solutions. We study the
impact of the deviation from exact resonance on the destabilizing modes and on
the final states. In regimes in which the mode interaction leads to traveling
waves our numerical simulations reveal localized waves in which the wavenumbers
are resonant and which drift through a steady background pattern that has an
off-resonant wavenumber ratio.
