In this work we intend to develop a systematic framework that appropriately reduces the initial system of CLEs to subsystems with similar time scales. Specifically, by applying an appropriate transformation to the original system, the initial state vector of the CLE system is decomposed to fast and slow subvariables. This allows for a non-stiff description by treating each set differently. A set of sufficient and necessary conditions arises, which has to be met to ensure the existence of the appropriate transformation. The second step is to treat each of the two subsets independently. We extend and apply the method of adiabatic elimination to the systems under consideration. Fast variables are assumed to relax to a pseudo-stationary density under the assumption that the slow variables remain constant. Slow variables are approximated through a Fokker-Plank equation which governs the probability density of only the slow variables. Ultimately the distribution of the slow variables can be sampled through the solutions of a system of CLEs that correspond only to the slow subspace. The final step is to compute the approximated solution of the initial CLEs system by simply multiplying the two independent probability densities. The rigorousness of the proposed framework will be examined through illustrative biological examples that lie in the continuous Markov process regime.