Two-dimensional spectral analysis is used to highlight periodiCities in regular lattice samples of insect spatial distributions. The technique is explained, and simulated distributions are analyzed to show how results are interpreted. Based on analyses of samples at one site, the distributions of gypsy moth larvae are characterized by wavelike periodicities and sometimes by small-scale clumping. The larvae of the gypsy moth predator Calosoma sycophanta L. exhibit regular, small-scale clumping. Adult C. sycophanta distributions vary between small-scale clumps and large-scale waves, sometimes showing both at once. These analyses are compared with calculations of Lloyd's patchiness index for the same distributions, with generally complementary results. Spectral analysis is a powerful and useful adjunct to other methods of measuring dispersion and should be useful in entomological research.