In the present work, we examine the propagation of weakly nonlinear waves in a prestressed thin viscoelastic tube filled with an incompressible inviscid fluid. Considering that the arteries are initially subjected to a large static transmural pressure P-0 and an axial stretch lambda(z) and, in the course of blood flow, a finite time dependent displacement is added to this initial field, the nonlinear equation governing the motion in the radial direction is obtained. Using the reductive perturbation technique, the propagation of weakly nonlinear waves in the long-wave approximation is studied. After obtaining the general equation in the long-wave approximation, by a proper scaling, it is shown that this general equation reduces to the well-know nonlinear evolution equations. Intensifying the effect of nonlinearity in the perturbation process, the modified forms of these evolution equations are also obtained.