Control of standing posture requires fusion of multiple inputs including visual, vestibular, somatosensory, and other sensors, each having distinct dynamics. The semicircular canals, for example, have a unique high-pass filter response to angular velocity, quickly sensing a step change in head rotational velocity followed by a decay. To stabilize gaze direction despite this decay, the central nervous system supplies a neural "velocity storage" integrator, a filter that extends the angular velocity signal. Similar filtering might contribute temporal dynamics to posture control, as suggested by some state estimation models. However, such filtering has not been tested explicitly. We propose that posture control indeed entails a neural integrator for sensory inputs, and we test its behavior with classic sensory perturbations: a rotating optokinetic stimulus to the visual system and a galvanic vestibular stimulus to the vestibular system. A simple model illustrates how these two inputs and body tilt sensors might produce a postural tilt response in the frontal plane. The model integrates these signals through a direct weighted sum of inputs, with or without an indirect pathway containing a neural integrator. Comparison with experimental data from healthy adult subjects (N = 16) reveals that the direct weighting model alone is insufficient to explain resulting postural transients, as measured by lateral tilt of the trunk. In contrast, the neural integrator, shared by sensory signals, produces the dynamics of both optokinetic and galvanic vestibular responses. These results suggest that posture control may involve both direct and indirect pathways, which filter sensory signals and make them compatible for sensory fusion.NEW & NOTEWORTHY Control of standing posture requires fusion of multiple inputs including visual, vestibular, somatosensory, and other sensors, each having distinct dynamics. We propose that postural control also entails a shared neural integrator. To test this theory, we perturbed standing subjects with classic sensory stimuli (optokinetic and galvanic vestibular stimulation) and found that our proposed shared filter reproduces the dynamics of subjects' postural responses.