Abyssal hills within 20 km of the Clipperton and Pitman transforms deviate from regional trends by as much as 15°–20°. We use a thin viscous sheet model with power-law rheology to test the hypothesis that these anomalous trends result from distributed deformation of oceanic lithosphere, probably associated with periods of transpression. The variation of abyssal-hill trends with distance from the transform matches model predictions, with power-law exponents consistent with lithospheric rheology controlled by a combination of slip on faults at shallow depths and ductile creep in deeper parts. Predicted displacements are less than actual slip along the transforms, suggesting that only part of relative plate motion is taken up by distributed deformation. These results suggest that abyssal-hill rotation is sporadic, occurring perhaps when physical conditions (e.g., pore-fluid pressure, hydrothermal alteration, or transpression) are particularly favorable.