This article reports on the development and tests of the Adaptative Semi-Implicit Scheme (ASIS) solver for the simulation of atmospheric chemistry. To solve the Ordinary Differential Equation systems associated with the time evolution of the species concentrations, ASIS adopts a one step linearized implicit scheme with specific treatments of the Jacobian of the chemical fluxes. It conserves mass and has a time stepping module to control the accuracy of the numerical solution. In idealized box model simulations ASIS gives results similar to the higher order implicit schemes derived from the Rosenbrock's and Gear's methods. When implemented in the MOCAGE CTM and the LMD Mars GCM the ASIS solver performs well and reveals weaknesses and limitations of the original semi-implicit solvers used by these two models. ASIS can be easily adapted to various chemical schemes and further developments are foreseen to increase its computational efficiency, and to include the computation of the concentrations of the species in aqueous phase in addition to gas phase chemistry.