Offshore infrastructure often interacts cyclically with the seabed over the operational life of a project. Previous research on the evolution of soilβs undrained strength under long term, large-amplitude cyclic loading has focused on contractile clays and demonstrated that this cyclic interaction can lead to the initial generation and later dissipation of positive excess pore pressure in the soil. This process generally leads to an initial strength reduction, with subsequent densification and soil strength gains that can have consequences on the performance of seabed infrastructure during its design life. In this paper, new experimental data from T-bar penetrometer testing in reconstituted kaolin and Gulf of Mexico clays is presented. The data illustrate how the stress history, quantified via the overconsolidation ratio, affects soil strength changes during large-amplitude cyclic loading. The experiments explore both long-term continuous loading cycles and episodic loading with packets of undrained cycles followed by quiescent consolidation periods. A critical state-based framework is used to interpret the experimental data and provide predictions of the long-term steady-state strength of both soils as a function of the initial in situ state of the soil.