It is shown that the contribution of higher harmonics to the lunar transfer functions for the tangential components of the surface magnetic field is significant at frequencies greater than 0.01 Hz (Apollo 12 and Explorer 35 magnetometer data extend to frequencies as high as 0.04 Hz). The inclusion of the higher harmonics shows that there are two distinct transfer functions corresponding to the components of the tangential surface magnetic field perpendicular and parallel to the direction of the wave vector of the external disturbance forcing the lunar induction. The dependences of these transfer functions on frequency and location are determined. The effects of the higher harmonics can (1) account for a hitherto unexplained feature in the Apollo 12 and Explorer 35 transfer functions, namely the rolloff at high frequencies, and (2) offer a possible explanation for the frequency dependence of the difference between the transfer functions for the two orthogonal components of the surface magnetic field. The harmonic response of a simple current layer model of the moon is derived and shown to provide a reasonable fit to the experimental data.