The equations for calculating the diffusion limiting current, i(lim), in steady-state voltammetry (known as the Peers equation in membrane science) and the transition time, tau, in chronopotentiometry (the Sand equation) are broadly used in electrode and membrane electrochemistry. The applicability of these equations is limited because they are deduced under the assumption of a constant diffusion coefficient. However, within the diffusion boundary layer, the diffusion coefficient, D, varies between the values corresponding to the bulk solution (D-b), and the infinitely dilute solution (D-0) near the electrode or membrane surface. In this paper, we explore two models, which account for the concentration dependence D(c) in order to generalise the above fundamental equations. We show that the correct value of i(lim) can be found via solution of a 2D model, while to find tau, a 1D non-stationary model is sufficient. Generally, the dependence of i(lim) on the bulk concentration deviates from the proportionality. The similar situation occurs with the proportionality of tau to the squared concentration in the Sand equation. We show that the numerical solutions for i(lim) and tau can be presented in the forms analogous to the Peers and the Sand equations, respectively, but with an additional correction factor. In particular, an effective diffusion coefficient, D-ef (an average between D-b and D-0) has to be introduced in the case of Sand equation. Comparison of our theoretical prediction with experimental chronopotentiograms confirms the necessity of taking into account the D(c) dependence. (C) 2016 Elsevier Ltd. All rights reserved.