A Doubly-Conditional Moment Closure (DCMC) solver was presented and used to providestructures of non-premixed counterflow flames of gaseous heptane against methane/airmixtures as the oxidizer in anticipation of future multi-dimensional turbulent combustioncalculations of dual-fuel systems. To supplement these calculations and to understand better thestructure of such flames, the same counterflow flames were simulated with Cantera. Twomethane/air equivalence ratios were considered, one below and one above the lean flammabilitylimit of the methane/air premixed mixture. The effect of flame straining was also investigatedby employing two strain rates: one far away from and one close to the critical extinction strainrate. The accuracy of the usual assumption of unity Lewis number employed by the DCMCsolver was examined using the Cantera simulations and it was concluded that somediscrepancies exist in intermediate species and temperature profiles compared to the case whendifferential diffusion was taken into account. These differences were enhanced by increasedstraining. The Le=1 model resulted in lower gradients of some species, which in turn resultedin lower scalar dissipation of the mixture fraction and progress variable. The heat release rateprofile of the flames implied the existence of two separate reaction zones, which merged at highstrain rates. The DCMC model predicted quite accurately the methane/air side of the flame inmixture fraction space, but not to the same degree of accuracy the heptane side of the flame.Moreover, it extended the methane consumption layer and as the strain rate of the flameincreased it overpredicted the maximum flame temperature