We present far-infrared and submillimetre spectra of three carbon-rich evolved objects, AFGL 2688, AFGL 618 and NGC 7027. The spectra were obtained with the SPIRE Fourier-transform spectrometer on board the Herschel Space Observatory, and cover wavelengths from 195-670 mu m, a region of the electromagnetic spectrum hitherto difficult to study in detail. The far infrared spectra of these objects are rich and complex, and we measure over 150 lines in each object. Lines due to 18 different species are detected. We determine physical conditions from observations of the rotational lines of several molecules, and present initial large velocity gradient models for AFGL 618. We detect water in AFGL 2688 for the first time, and confirm its presence in AFGL 618 in both ortho and para forms. In addition, we report the detection of the J = 1-0 line of CH+ in NGC 7027.