Dynamic modelling of electrochemical systems in the time-domain generally requires the inversion of Laplace transforms. Unfortunately, many practical systems exist for which the inverse transforms cannot be derived analytically. A new approach of the dynamics of electrochemical systems, investigated under small-signal conditions, is proposed in this work. The method is based on numerical inversion of Laplace transforms and, more especially, on the Gaver–Stehfest (GS) inversion formula. General and explicit formulations of the time-domain responses of stable systems to a small potential step/ramp and to a small current step/pulse are derived in part I of this work from linear combinations of values of the system immittance that is the admittance for potential-controlled techniques and the impedance for current-controlled techniques. The GS approach of system dynamics is illustrated by taking the example of finite-space diffusion of electroactive species. Application to corrosion systems, polymer exchange membrane fuel cells and thin-film ion-insertion electrodes will be presented in the next parts of this work.