Two different curvilinear, flame coordinate systems are introduced. These form the basis for either the Intrinsic Disturbed Flame Equations (IDFE) or the Strongly Stretched Flamelet Equations (SSFE), which are quasi-one-dimensional systems of differential equations describing the inner structure and propagation velocity of stretched, premixed flames. Integral analysis is applied to derive relations for the mass burning rate, and for the IDFE, to derive jump conditions. The feasibility of both descriptions has been demonstrated. Finally, an efficient solution strategy for premixed flames is proposed, that combines both formalisms.