In this work we propose new algorithms for space time nonlinear reactive transport. They conjugate the versatility of Optimized Schwarz Waveform Relaxation, permitting adaptive time stepping, and the fast convergence of Newton algorithms. We present three approaches which differ in the order of combination of Newton's method and the Schwarz waveform relaxation algorithm. In the new approaches, the arising linear systems are treated by an inexact Krylov-type method. Numerical tests in 2D study the influence of the parameter of the Robin transmission condition. They prove that both approaches provide a considerable acceleration of the convergence speed. We provide also results in 3D for a two species nonlinear coupled reactive transport system in the context of CO2 geological storage simulation.