In this paper, we show that iterative substructuring methods of Finite Element Tearing and Interconnecting type can be successfully employed for the solution of linear systems arising from the finite element approximation of scalar advection-diffusion problems. Using similar ideas as those of a recently developed Neumann-Neumann method, we propose a one-level algorithm and a class of two-level algorithms, obtained by suitably modifying the local problems on the subdomains. We present some numerical results for some significant test cases. Our methods appear to be optimal for flows without closed streamlines and possibly very small values of the viscosity. They also show very good performances for rotating flows and moderate Reynolds numbers. Therefore, the algorithms proposed appear to be well-suited for many convection-dominated problems of practical interest.