Alluvial river systems respond to changing sea level by adjusting channel length through shoreline translation and coastal onlap/offlap at the alluvial basement transition. The magnitude and timing of shoreline translation and coastal onlap/offlap relative to the driving sea level signal depend on the dynamics of the fluvial system and have important implications for interpreting ancient fluviodeltaic deposits. I obtain analytical solutions to a diffusive geometric model of fluviodeltaic response to sea level perturbations that treats the shoreline and alluvial basement transition as moving boundaries. Fluviodeltaic behavior is most sensitive to the ratio of the period of eustatic cycling to the fluvial response time, which varies with the length and water discharge of the fluvial system. The square root of this ratio provides a first-order estimate of the fraction of the fluvial long profile affected by eustatic forcing. The fluviodeltaic system behaves as a low-pass filter with respect to eustatic cycling: The amplitude of both shoreline translation and coastal onlap/offlap increase with increasing cycle period within a relatively narrow bandwidth in which the fluvial response time is comparable to the cycle period. Only small time lags develop between shoreline response and eustatic forcing. The time lag between maximum coastal onlap and maximum sea level increases without bound as the forcing period decreases relative to the fluvial response time. Model predictions agree with experimental data and differ considerably from the model predictions of Pitman (1978) and Angevine (1989), which suggest that fluviodeltaic systems are strong high-pass filters to sea level cycling.