Abstract. We present a new global Chemical Transport Model (CTM) with full stratospheric chemistry and Lagrangian transport and mixing called ATLAS (Alfred Wegener InsTitute LAgrangian Chemistry/Transport System). Lagrangian (trajectory-based) models have several important advantages over conventional Eulerian (grid-based) models, including the absence of spurious numerical diffusion, efficient code parallelization and no limitation of the largest time step by the Courant-Friedrichs-Lewy criterion. The basic concept of transport and mixing is similar to the approach in the commonly used CLaMS model. Several aspects of the model are different from CLaMS and are introduced and validated here, including a different mixing algorithm for lower resolutions which is less diffusive and agrees better with observations with the same mixing parameters. In addition, values for the vertical and horizontal stratospheric bulk diffusion coefficients are inferred and compared to other studies. This work focusses on the description of the dynamical part of the model and the validation of the mixing algorithm. The chemistry module, which contains 49 species, 170 reactions and a detailed treatment of heterogeneous chemistry, will be presented in a separate paper.