A longstanding goal of systems neuroscience is to quantitatively describe how the brain integrates sensory cues over time. Here we develop a closed-loop orienting paradigm in Drosophila to study the algorithms by which cues from two modalities are integrated during ongoing behavior. We find that flies exhibit two behaviors when presented simultaneously with an attractive visual stripe and aversive wind cue. First, flies perform a turn sequence where they initially turn away from the wind and but later turn back toward the stripe, suggesting dynamic sensory processing. Second, turns toward the stripe are slowed by the presence of competing wind, suggesting summation of turning drives. We develop a model in which signals each modality are filtered in space and time to generate turn commands, then summed to produce ongoing orienting behavior. This computational framework correctly predicts behavioral dynamics for a range of stimulus intensities and spatial arrangements.