In today's modeling and analysis of electrochemical cycling of Li- and Na-ion batteries, an assumption is often made regarding the interphase that forms between the active material and liquid electrolyte at low potentials, the so-called solid-electrolyte interphase (SEI). The SEI is generally assumed to act like an Ohmic resistor despite its complex chemical composition and porosity distribution. Here, one reports that this assumption does not hold for alkali-ion batteries. The SEI possesses a non-linear overpotential characteristic which saturates already at low current density of 0.1 mA cm(-2) giving only 3.3 +/- 1 mV for Li- metal electrodes in different electrolytes. For Na- and K-metal electrodes, these SEI overpotentials become dominating with 31 mV and 72 mV at the same low current densities giving significant disadvantages over Li-ion batteries for commercial applications. With the introduction of a new term, one achieves agreement between the parameters from galvanostatic cycling and electrochemical impedance spectroscopy for the first time. The discovery of the non-linear SEI overpotential disrupts the general believes about the role of the SEI for today's batteries as it is basically negligible for Li-ion batteries at room temperature. (C) 2017 Elsevier Ltd. All rights reserved.