Mixing and combustion in supersonic reacting §ows are currently under investigation for new generation launchers and trans-atmospheric vehicles. Experimental results with hydrogen injected at Mach 2.5 in a Mach 2 airstreams showed combustion taking place just in ∼ 0.6 m: this indicates that supersonic combustion is feasible within short combustors. Large eddy numerical simulations including the subgrid scale (SGS) model, ISCM, developed speci¦cally for supersonic combustion have been done. This model takes into account the e¨ect of compressibility on reaction rates and on mixing. Numerical simulations have revealed that the §ame is unsteady: it anchors at about 15 cm from the injector, develops downstream, and lifts o¨. Periodical ignition and quenching have been investigated. Also, the combustion regime in supersonic §ows has been investigated and is reported.