Analysis of foundation behaviour under repeated loading can be important to the design of offshore facilities, towers, bridges, wind turbines and other structures. Although detailed guidance is available on how some geomaterials behave under cycling, few such studies have been reported on the glacial formations that are widespread across parts of northern Europe and under the North and Baltic Seas. This paper presents a cyclic laboratory investigation involving block samples of Bolders Bank till, which is one of the most extensive North Sea glacial formations. Static and cyclic triaxial tests are reported on nominally identical, low-plasticity, high-overconsolidation-ratio specimens from Cowden, near Hull in the UK. Twenty-three cyclic tests are reported on specimens that were re-consolidated to K<jats:sub>0</jats:sub> stresses before experiencing up to 3500 undrained cycles involving a range of mean and cyclic shear stress combinations. The impacts of cycling on effective stress paths and strain development, cyclic stiffness and damping ratios are reported and interpreted with respect to parallel index, oedometer and monotonic triaxial compression and extension tests. Stable, metastable and unstable patterns of behaviour are identified, along with different cyclic failure modes. The styles of cyclic response are related to the till's static yielding behaviour. While the till can only manifest quasi-elastic behaviour within a very small (Y<jats:sub>1</jats:sub>) kinematic yield surface (KYS), a larger second (Y<jats:sub>2</jats:sub>) KYS is identified within which repeated loading leads to a non-linear yet stable response, with negligible mean effective stress drifts or stiffness degradation with low and stabilising strain accumulation rates. Cyclic paths that engage and relocate the Y<jats:sub>2</jats:sub> surface lead to greater permanent strains, mean effective stress drifts and stiffness decays that become progressively more marked as the magnitudes of the cyclic stress perturbation and the number of cycles increase. While cycling under stable or metastable conditions increased the ultimate undrained strength of specimens that did not develop excessive strains, most cyclic paths that exceeded and climbed the till's Hvorslev surface were unstable and eventually failed. The experiments identified the key factors that affect the till's response to repeated loading and provide a basis for developing, testing and calibrating cyclic constitutive models and establishing simplified design procedures for comparable tills.