Measurements of the nonlinear response of the basilar membrane to a pure tone are shown to have a simple form for moderate membrane velocities:   V(x,f;Vu)/Vu≈[Ṽ(x,f)/Vu]ν(x,f), f⩽fc(x),where the responseVis the velocity of the membrane at measurement positionx,Vuis the umbo velocity,fis the frequency of the stimulus, andfc(x)is the local characteristic frequency. The frequency dependence of the functionsν(x,f)andṼ(x,f)is determined from the data, andν(x,f)andln Ṽ(x,f)are shown to be analytic functions in the lower half of the complex frequency plane, withRe{ν(x,f)}a monotonically increasing function offat fixedx. The linear limit of basilar membrane motion is characterized by a transfer functionT(x,f)=(Ṽ/V1)ν/(1−ν),estimated by extrapolatingV(x,f;Vu)/Vuto a small membrane velocityV1.T(x,f)andln T(x,f)are shown to be analytic functions in the lower half of the complex frequency plane. The inverse of the amplitude of the transfer function, which has both a deep dip atf≈fc(x)and a broad shoulder at lower frequencies, bears a striking resemblance to the neural threshold tuning curve. The functional form ofT(x,f)is used todeducethe equation governing the motion of a section of the organ of Corti. Each section acts like anegativelydamped harmonic oscillator stabilized at timetby a feedback force proportional to the velocity at the previous timet−τ.The time delay τ is proportional to the oscillator period[τ=1.75/fc(x)].Like a laser, the organ of Corti pumps energy into harmonic traveling waves. Unlike the laser, the direction of energy flow abruptly reverses as the traveling wave approaches the point of maximum membrane velocity[fc(x)≈f].All accumulated wave energy is then pumped back into a small section of the organ of Corti where transduction presumably occurs. Outer hair cells are conjectured to be active elements contributing to the negative damping and feedback of the cochlear amplifier.