We show that the non-linear response of certain direct gap semiconductor superlattices is greatly enhanced when the separation of the lowest conduction bands is comparable with the magnitude of the principal gap. The mechanism which results in this enhancement is virtual transitions to higher subbands. Examples of (InAs)l-,(GaSb),/AlSb superlattices expected to exhibit the enhanced non-linear response in the near-infrared region of the spectrum are presented. We also investigate non-linear response in semiconductor superlattices at ultrashort times (-100 fs). In our scheme a full account is given for the first time of band structure effects upon transients. We then use a three-level model to determine the conditions under which predictions, based on the steady-state response theory and the golden rule, break down in structures with closely spaced energy levels.