Due to limited possibilities of experimental investigations for non-equilibrium gas flows, numerical results are of highest interest. Although the well-established Direct Simulation Monte Carlo (DSMC) method achieves highly accurate solutions, the computational requirements increase excessively for lower Knudsen regimes. Computationally more efficient simulations can be achieved with stochastic continuum-based methods using either the Bhatnagar-Gross-Krook (BGK) or the Fokker-Planck (FP) approximations where, instead of particle collisions, particle relaxation processes are considered. This paper explains the implementation of different stochastic BGK and FP methods in the open-source particle code PICLas for multi-species molecular gas flows. For verification, the results of different test cases are compared.