Generally, when velocity filters are applied to prestack seismic data, they can suppress long-period multiples, but they can also deteriorate the primary amplitudes. Since the apparent velocity differences between primaries and multiples can be negligible within the near-offset regions of data gathers, a velocity filter will be ineffective in these regions, tending to remove or distort primary signal. The normal solution to this problem is to mute or remove near-offset data, but this approach is detrimental to low-fold data. In this paper, we derive a filter that can be used to address the problem by responding to average apparent velocity differences rather than to instantaneous apparent velocity differences between primaries and multiples. The filter, called a local coherence filter, is essentially a finite-difference operator whose step size is equivalent to a spatial prediction distance. Within the local coherence filter's small application window, an NMO-corrected multiple is predictable while an overcorrected primary is not predictable. The step size of its difference operator gives the filter the ability to discriminate between primaries and long-period multiples in regions of a data gather where velocity filters fail. This paper derives the local coherence filter and compares it to the f-k filter in both model and real-data applications. Results demonstrate that the local coherence filter is more effective in suppressing long-period multiples without distorting the primary reflections.