The frequency dependence of second-harmonic generation (SHG) at an adsorbate-covered semiconductor surface is investigated. A one-dimensional model is proposed for the bulk carrier motion in the vicinity of the adsorbate. Numerical simulations were performed for the cases of carriers induced by charge transfer from strong donor- or acceptor-type adsorbates. The SHG spectra reveal strong resonant signal enhancement resulting from Rydberg-like states of the carrier-surface system.