Abstract <p>We investigate the optical properties of guided-mode resonant gratings with the thickness of the waveguide layer spatially varying according to a parabolic law. We show that an efficient approach for describing such structures is the coupled-mode theory (CMT) with varying parameters. The CMT simulations are quite fast and its predictions turn out to be in a good agreement with time-consuming rigorous simulations based on the aperiodic Fourier modal method. We demonstrate that the optical properties of gratings with convex and concave waveguide layers are quite different, which is explained in terms of the local photonic band gap of the considered structures. In our opinion, the obtained results are promising for the design of optical filters and resonators based on quasiperiodic photonic structures with nonlinearly varying parameters.</p>