We consider a singularly perturbed two-dimensional convection-diffusion problem in a rectangle with flow parallel to the x-axis. On the inflow and outflow boundaries Dirichlet type conditions are imposed and on the characteristic boundaries regular Robin type conditions (including the possibility of Neumann conditions) are given. For small values of the parameter e, regular (strong) and parabolic (weak) layers appear. In this case the parabolic layers do not involve the first term of the asymptotic expansion. For the proposed problem, e-uniformly convergent methods are considered. Note, that for the upwind finite difference scheme the order of e-uniform convergence does not exceed one. Using the High Order Compact (HOC) standard technique, we construct a classical method on piecewise uniform Shishkin meshes having uniform convergence with order 3/2 in the maximum norm. Numerical results are presented and discussed.