Four zero-phonon lines of defect centres in diamond (GR1 (741 nm), N-V (637 nm), H4 (496 nm) and N3 (415 nm)) have been shown to exhibit persistent spectral hole burning. The phenomenon appears to be a rather general one in diamond and should prove very powerful for elucidation of the nature of defect centres. As an example, preliminary results for the N-V centre suggest a previously undetected splitting of the excited state.