The three-state kinetic model developed in our previous paper (R. Guidelli and L. Becucci, 2016), which explains all the main features of experimental current-voltage curves of peptide ion channels at conventional bilayer lipid membranes (BLMs), is extended to explain some still unsettled features of the corresponding voltage-step current-time (I-t) curves. To this end, the time dependence of the open probability of peptide ion channels during the first few seconds from the instant of the voltage step, before the attainment of its steady-state value expressed by the well-known one-sided Boltzmann equation, is taken into account. This approach explains the reason for the different behavior of the experimental sigmoidal I-t curves with respect to the wholly concave downward ones; the frequent occurrence of concave downward I-t curves characterized by a time course describable by a sum of two exponential functions is also justified. On the other hand, the three-state kinetic model disproves the validity of the experimental procedure aiming at estimating the gating charge of peptide ion channels from the initial stage of the time derivative of ON and OFF ionic currents, commonly justified by an unproved analogy with gating currents of potassium ion channels. (C) 2018 Elsevier Ltd. All rights reserved.