A range of planform morphologies emerge along sandy coastlines as a function of offshore wave climate. It has been implicitly assumed that the morphological response time is rapid compared to the timescales of wave climate change, meaning that coastal morphologies simply reflect the extant wave climate. This assumption has been explored by focussing on the response of two distinctive morphological coastlines – flying spits and cuspate capes – to changing wave climates, using a coastline evolution model. Results indicate that antecedent conditions are important in determining the evolution of morphologies, and that sandy coastlines can demonstrate hysteresis behaviour. In particular, antecedent morphology is particularly important in the evolution of flying spits, with characteristic timescales of morphological adjustment on the order of centuries for large spits. Characteristic timescales vary with the square of aspect ratios of capes and spits; for spits, these timescales are an order of magnitude longer than for capes (centuries vs. decades). When wave climates change more slowly than the relevant characteristic timescales, coastlines are able to adjust in a quasi-equilibrium manner. Our results have important implications for the management of sandy coastlines where decisions may be implicitly and incorrectly based on the assumption that present-day coastlines are in equilibrium with current conditions.