The nonlocal theory of electrostatic density drift instabilities is developed for an arbitrary, periodic variation in plasma density. Linear Vlasov theory is applied to Fourier series representations of the plasma density, and the resulting equations are solved numerically. The growth rates of the universal drift instability are compared by using local and nonlocal theories. It is demonstrated that the local theory is inadequate if the nonlocal eigenfunctions of the electrostatic modes have significant amplitude over sptial regions wider than the regions of large plasma density gradients. Nonlocal effects can enhance wave-particle of a triangular-shaped variation and reduce wave-particle dissipation of a square-shaped irregularity.