The parabolized stability equations (PSE) are used to investigate issues of nonlinear flow development and mixing in compressible reacting shear layers, which are modelled with an infinitely fast-chemistry assumption. Particular emphasis is placed on investigating the change in flow structure that occurs when compressibility and heat release are added to the flow. These conditions allow the ‘outer’ instability modes – one associated with each of the fast and slow streams – to dominate over the ‘central’, Kelvin–Helmholtz mode that exists unaccompanied in incompressible non-reacting mixing layers. Analysis of scalar probability density functions in flows with dominant outer modes demonstrates the ineffective, one-sided nature of mixing that accompanies these flow structures. Colayer conditions, where two modes have equal growth rate and the mixing layer is formed by two sets of vortices, offer some opportunity for mixing enhancement. Their extent, however, is found to be limited in the mixing layer's parameter space. Extensive validation of the PSE technique also provides a unique perspective on central-mode vortex pairing, further supporting the view that pairing is primarily governed by instability growth rates; mutual induction appears to be a secondary process. This perspective sheds light on how linear stability theory is able to provide such an accurate prediction of experimentally observed, fully nonlinear flow phenomenon.