Modifications of the multigrid method for solving heat and mass transfer problems are offered. Strongly nonsymmetric systems of the linear algebraic equations obtained after difference approximation of the convection-diffusion equation with dominant convection are considered. The choice of MGM-smoothers from the class of triangular and alternately-triangular skew-symmetric iterative methods is researched. Results of the Fourier-analysis of the MGM modifications are presented. Heat transfer and mass transfer are kinetic processes that may occur and be studied separately or jointly. Studying them apart is simpler, but both processes are modeled by similar mathematical equations in the case of diffusion and convection, and it is thus more efficient to consider them jointly. Mathematical models that involve a combination of convective and diffusive processes are among the most widespread in all the sciences. Research of these processes is especially important and difficult when convection is dominant. At the same time, convection-diffusion equations are used as tests in researching iterative methods for solving systems of strongly nonsymmetric linear equations. The choice of discretization method is very important for partial differential equation with the first order derivatives. Applying upwind differences, we can obtain an M-matrix, and using central differences, we can get a positive real or dissipative matrix. We have used central-difference approximation of convective terms. In this case, the resulting system of linear algebraic equations is a strongly nonsymmetric one. A special class of triangular skew-symmetric iteration methods is intended for these types of systems. We have used the triangular iterative methods (TIMs) from this class as smoothers in multigrid method (MGM) for the solution of the linear algebraic equation system with a strongly nonsymmetric matrix obtained after central-difference approximation of the convection-diffusion equation with dominant convection. Multigrid methods are proving themselves as very successful tools for the solution of the different problems. The key to the efficiency of multigrid method is the "correct" choice of its components and effective interaction between smoothing and coarse-grid correction. We need to use special iterative methods as a smoother for the multigrid method and non-standard course-grid correction for a good approximation of the smooth error components. Fourier analysis is the main tool for quantitative estimates.