Abstract In this study we examine glaciogenic rhythmites from the Late Palaeozoic Itararé Group, Paraná Basin, Brazil. We conduct spectral analysis on lithological cycle (‘couplet’) thickness series, and declination of maximum axis of anisotropy of magnetic susceptibility ellipsoidal tensor (K1) data. We tested the efficiency of K1 as a palaeoclimatic proxy. To constrain the timescale of harmonic features in the data, we analysed the couplet thickness spectra, converting the spectra to the time domain using an astronomical calibration based on Milankovitch frequency ratios. Comparison of the two rhythmites provides insights into their sedimentation rate evolution and cyclicity. Millennial-scale mechanisms of climatic origin influenced the deposition of both rhythmites, generating the lithological couplets, and are consistent with millennial-scale variations recognized as triggers for large-scale climatic changes during the Late Pleistocene. The common harmonic features in the couplet thickness and K1 spectra support the view that the azimuth of the K1 axis in sedimentary fabric is a useful palaeoclimatic proxy, reflecting sedimentation processes that were directly influenced by flow-induced, sediment transport, which is linked to external climate factors.