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This paper presents quasi-analytical solutions of river water quality modelling approach that integrates QUAL2E pollutant transformation ODEs in to dynamic CSTR method as an improvement over the numerical solution approaches used in conceptual water quality models. We compared it with the Euler method implemented in the widely applied SWAT model and explicit as well as implicit fourth order Rung-Kuta methods implemented in conceptual water quality models such as QUASAR and QUESTOR. The improvement mainly aimed at increasing model accuracy and solution stability with special emphasis for simulations during the low flow periods. We evaluated the behaviors of results from the Euler numerical solutions and the Runge Kuta4 numerical integration methods. It turned out that the numerical methods show serious instability for large residence times because of overestimations of decay processes. To overcome the instability we derived, based on simplifying assumptions, quasi-analytical solutions of inhomogeneous first order differential equations resulting from integration of the QUAL2E transformation formulations in to the CSTR-based mass balance equations. Finally, we tested the stability of the quasi-analytical method for real simulations and hypothetical extreme low flow scenarios. The new quasi-analytical solution gives unconditionally stable solution even when advanced implicit fourth order Rung-Kuta schemes give unstable results. It also gives fairly comparable results with the reference RWQM while running 130,000 times faster than it. Water quality processes are so critical during the low flow periods that it is fair to conclude that this approach is preferable to the numerical solutions of solute transformation ODEs. Besides the riverine system, this approach is well suited for water quality modelling in conveyance systems associated with large residence times like navigation canals. Furthermore, we demonstrated that the dynamic quasi-analytical CSTR solution of non-conservative pollutant modelling is analogous to the classical steady linear reservoir approach with variable and residence-time-dependent reservoir constant.