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Three-dimensional laminar flow structures with mixing, chemical reaction, normal strain, and shear strain qualitatively representative of turbulent combustion at the small scales are analyzed. A mixing layer is subjected to counterflow in the transverse y- and z-directions. Both non-reactive and reactive flows are examined. Reduction of the three-dimensional boundary-layer equations to a one-dimensional similar form is obtained allowing for heat and mass diffusion with variations in density and properties. In steady configurations, a set of ODEs governs the three velocity components as well as the scalar-field variables. A flamelet model for individual diffusion flames with combined shear and normal strain is developed. Another model with solution in similar form is obtained for a configuration with a dominant diffusion flame and a weaker fuel-rich premixed flame. Results for the velocity and scalar fields are found for ranges of Damkohler number Da, normal strain rate due to the counterflow, streamwise-velocity ratio across the mixing layer, Prandtl number, and Mach number. For the flamelet model, a conserved scalar is cast as the independent variable to give an alternative description of the results. The imposed normal strain decreases mixing-layer thickness and increases scalar gradients and transport rates. There is indication of diffusion control for partially premixed flames in the multi-branched flame situation. The enhancement of the mixing and combustion rates by imposed normal strain on a shear layer can be very substantial. Also, the imposition of shear strain and thereby vorticity on the counterflow can be substantial indicating the need for flamelet models with both shear strain and normal strain.