An effective reduction method based on geometric singular perturbation and center manifold techniques is proposed. This method eliminates the fast and stable dynamics and gives the equations describing the slow ones. It is coordinate-free and extends the well-known quasi-steady-state method classically used for kinetic scheme reduction. This yields directly the slow dynamics even if the differential equations are not in standard two time-scale form (Tikhonov form). Application to combustion kinetics including 13 species and 67 reactions is presented and simulations are given.