Abstract Burning velocities of a number of slow-burning, fuel-rich hydrogen + nitrogen + oxygen flames have been measured and compared with values computed on the basis of the chemical mechanism proposed by Dixon-Lewis (1970a). This mechanism is shown to be incomplete, and in order to obtain agreement between theory and experiment over the composition range studied, it is necessary to invoke some further chain breaking steps involving hydroxyl radicals and oxygen atoms. The steps which have been considered lead to the extended mechanism OH + H2 ⇌ H2O + H, (i) H + O2 = OH + O, (ii) O + H2 ⇌ OH + H, (iii) H + O2 + M = HO2 + M, (iv) H + HO2 = OH + OH, (vii) H + HO2 = O + H2O, (viia) H + HO2 = H2+ O2, (xii) OH + HO2 = H2O + O2, (xiii) O = HO2 = OH +O2, (xiv) H + H + M = H2 + M, (xv) H + OH + M = H2O + M, (xvi) H + O + M = OH + M, (xvii) With the use of steady-state approximations for the small concentrations of OH and O present in the flames, the important new parameters in the analysis are k16, k17, and the ratios k7/k12, k7a/k12, k13/k12 and k14/k12. Although the number of these precludes an unambiguous assignment of values to them, numerical experimentation on reasonable assumed values of k15, k16 and k17 has led to the conclusions that: (a) The ratio (k7 +k7a)/k12 lies in the range 6.5 ± 1.0, assumed independent of temperature in the flame reaction zone. (b) The ratio k7/k7a is unlikely to be much greater than 0.1, and it may be much less than this. (c) Assumingk7a = k14 = 0, a maximum possible value of k137/k12 = 5.5 may be deduced from the dependence of burning velocity on composition. A further important feature shown by the computation is that for the imposed condition of satisfactory prediction of measured burning velocities, the hydrogen-atom concentration profiles in specific flames are not appreciably affected by the particular combination selected from the six adjustable parameters given above. In this context the more important parameters, apart from k15 (Dixon-Lewis 1970a), are shown to be the ratios 2k2/k4. Also in connexion with the atom and radical concentrations, a comparison of measured profiles of the relative intensity of chemiluminescence when traces of sodium salts are added to three of the flames studied, with profiles derived from the computed H and OH radical concentrations, leads to the conclusion that reaction (xix) is some 25 times faster than reaction (xviii) H + H + Na = H2 + Na*, (xviii) H + OH + Na = H2O + Na*. (xix) Lastly, the satisfactory prediction of the burning velocity of a much faster and hotter flame than those concerned in the bulk of the investigation provides further very powerful support for the reaction mechanism involving participation of hydroperoxyl. Effects of thermal diffusion in this and the other flames are discussed.