The aim of this paper is to propose an adaptation of the well known adaptive conformal inference (ACI) algorithm to achieve finite-sample coverage guarantees in multi-step ahead time-series forecasting in the online setting. ACI dynamically adjusts significance levels, and comes with finite-sample guarantees on coverage, even for non-exchangeable data. Our multi-step ahead ACI procedure inherits these guarantees at each prediction step, as well as for the overall error rate. The multi-step ahead ACI algorithm can be used with different target error and learning rates at different prediction steps, which is illustrated in our numerical examples, where we employ a version of the confromalised ridge regression algorithm, adapted to multi-input multi-output forecasting. The examples serve to show how the method works in practice, illustrating the effect of variable target error and learning rates for different prediction steps, which suggests that a balance may be struck between efficiency (interval width) and coverage.t