Methods are presented for analyzing the low-order stimulus-response cross-correlation functions (or kernels) of visual neurons studied with spatiotemporal white noise. In particular, formulas are derived that relate the low-order kernels of a cell to its responses to single-drifting, double-drifting, and counterphase gratings. The harmonic response terms contributed by the low-order kernels include a mean response term, first- and second-harmonic terms, and sum- and difference-harmonic terms. Using the formulas in this paper, one can obtain kernel-based predictions for the spatiotemporal-frequency tuning of each harmonic. These kernel-based predictions can then be compared with harmonic tuning data obtained in experiments with real grating stimuli. The methods are illustrated using data recorded from one simple and one complex cell from the primary visual cortex of the monkey. The approach of transforming low-order kernels into predicted harmonic tuning functions provides a useful data reduction technique as well as providing insight into the interpretation of kernels.