The rhythmically bedded limestone-marl alternations in the coastal cliffs of Sopelana and Zumaia in the Basque country, northern Spain, permit testing and refining of existing Maastrichtian chronologies (latest Cretaceous). The recently established astronomical time scale for the late Maastrichtian at Zumaia is extended into C31n with the integrated stratigraphy of the Sopelana section. The cyclic alternations of hemipelagic limestones and marls at Sopelana show a strong influence of eccentricity-modulated precession. Together, the Zumaia and Sopelana sections span almost the entire Maastrichtian, and encompass thirteen 405kyr cycles, spanning a total duration of 5.3Myr. From the K/Pg boundary downwards, 405kyr minima in the lithological, magnetic susceptibility and reflectance data records are tuned to successive 405kyr minima in the new La2011 eccentricity solution. Assuming a K/Pg boundary age of 65.97Ma, we present orbitally tuned ages of biostratigraphic and magnetostratigraphic events. While the bases of Chrons C29r and C30n were reliably established at Zumaia and are in good agreement with previous studies, new data from Sopelana provide a refinement of the basal age of Chron C31r. Additional planktonic foraminifera and calcareous nannoplankton data from Zumaia, and new calcareous nannoplankton data from Sopelana allow for worldwide correlation of the cyclostratigraphy of the Basque country. Supplementary materials: Identification of the 405 kyr minima; Geologic map; Paleomagnetic results; Sopelana data; Redfit 3.8 power spectra (.pdf); data tables (.rtf)