A modified inelastic electron tunnelling spectrometer is described which enables data to be stored in digital form in a microcomputer. Subsequent numerical analysis may then be carried out with considerable flexibility and convenience. Presentation of data is possible, not only in second derivative form as in a conventional spectrometer, but also as a third derivative by a simple numerical technique. Examples of data presented in both forms are given for a tunnel junction consisting of AI/AlO,/benzoic acid/Pb. In addition, the third derivative technique is used to subtract a rising background from the second derivative spectrum of an AI/AlO,/benzoic acidlhu tunnel junction.