If striate cells had the simple bipartite or tripartite receptive fields (RF's) classically attributed to them, they should be quite broadly tuned for spatial frequency. Most striate-cortex cells, however, are fairly narrowly tuned and would be expected to have more-periodic RF's. We have examined this question in recordings of the responses of cat and monkey striate-cortex cells to gratings of increasingly large number of cycles, all centered on the cells' RF's. Simple cells narrowly tuned for spatial frequency were found to increase their responses with increasing numbers of stimulus cycles beyond the 1 1/2 cycles expected from the classical RF shape. Broadly tuned simple cells were found to have less-periodic RF's. Whereas narrowly tuned complex cells were also found to respond maximally to many stimulus cycles, other more broadly tuned complex cells did as well (possibly reflecting summation across many broadly tuned simple cells without regard to phase). A suppressive region was often seen just outside the excitatory two-dimensional spatial-frequency region, at off orientations and/or off spatial frequencies and around the whole RF in space. Most striate cells can thus be described as having periodic RF's in the space domain such that they fire just to patterns whose local spatial-frequency spectra fall within a compact, restricted, roughly circular two-dimensional spatial-frequency region, with an encircling suppressive region in both the space and the frequency domains.