Non-Newtonian fluids such as blood, colloids, and cell suspensions are often manipulated in microfluidic devices and exhibit extraordinary flow behaviors, not existing in Newtonian fluids. This paper represents an analytical solution of transient velocity for electroosmotic flow of generalized Maxwell fluids through both a micro-parallel channel and a microtube, using the method of Laplace transform. The solution involves analytically solving the linearlized Poisson-Boltzmann equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations, the influence of normalized relaxation time on transient EOF velocity is investigated for different parametric values. (C) 2012 Elsevier B.V. All rights reserved.