The qualitative system analysis and model reduction for reacting flows has gained an increasing interest during the last years. Nowadays, simulations based on sophisticated algorithms implemented on powerful workstations turn out to be a prevailing tool of the system analysis. However, modelling of realistic systems of technical importance leads to an extreme growth of mathematical models both in complexity and in dimension, i.e. they become not treatable even by modern computational facilities. Recently, the concept of invariant, slow/fast -, attractive and stable manifolds, which appear in the system state space as a manifestation of a restricted number of degrees of freedom exhibiting by the system, has proven to be an efficient tool of system analysis and model reduction. In the current work questions about the specific low-dimensional manifolds’ identification, the analysis of their properties, their approximation and the application to model reduction of complex reacting flow systems is discussed.