The discontinuous Galerkin (DG) methods designed for hyperbolic problems arising from a wide range ofapplications are known to enjoy many computational advantages. DG methods coupled with strong-stabilitypreserving explicitRunge-Kutta discontinuous Galerkin (RKDG)time discretizations provide a robust numerical approach suitable for geoscience applications including atmosphericmodeling.However, a major drawback of the RKDG method is its stringent Courant-Friedrichs-Lewy (CFL) stability restriction associated with explicit time stepping. To address this issue, the authors adopt a dimension-splitting approach where a semi-Lagrangian (SL) time-stepping strategy is combined with the DG method. The resulting SLDG scheme employs a sequence of 1D operations for solving multidimensional transport equations. The SLDGscheme is inherently conservative and has the option to incorporate a local positivity-preserving filter for tracers.Anovel feature of the SLDGalgorithm is that it can be used for multitracer transport for globalmodels employing spectral-element grids, without using an additional finite-volume grid system. The quality of the proposed method is demonstrated via benchmark tests on Cartesian and cubed-sphere geometry, which employs nonorthogonal, curvilinear coordinates.