The dynamics of some elementary reactions of N(²D), C(³P,¹D) and CN(X²Σ⁺) of importance in combustion have been investigated by using the crossed molecular beam scattering method with mass spectrometric detection. The novel capability of producing intense, continuous beams of the radical reagents by a radio-frequency discharge beam source was exploited. From angular and velocity distribution measurements obtained in the laboratory frame, primary reaction products have been identified and their angular and translational energy distributions in the center-of-mass system, as well as branching ratios, have been derived. The dominant N/H exchange channel has been examined in the reaction N(²D) + CH₄, which is found to lead to H + CH₂NH (methylenimine) and H + CH₃N (methylnitrene); no H₂ elimination is observed. In the reaction N(²D) + H₂O the N/H exchange channel has been found to occur ia two competing pathways leading to HNO + H and HON + H, while formation of NO + H₂ is negligible. Formation of H + H₂CCCH (propargyl) is the dominant pathway, at low collision energy (E_c), of the C(³P) + C₂H₄ reaction, while at high E_c formation of the less stable C₃H₃ isomers (cyclopropenyl and/or propyn-1-yl) also occurs; the H₂ elimination channel is negligible. The H elimination channel has also been found to be the dominant pathway in the C(³P,¹D) + CH₃CCH reaction leading to C₄H₃ isomers and, again, no H₂ elimination has been observed to occur. In contrast, both H and H₂ elimination, leading in comparable ratio to C₃H + H and C₃(X¹Σ_g⁺) + H₂(X¹Σ_g⁺), respectively, have been observed in the reaction C(³P) + C₂H₂(X¹Σ_g⁺). The occurrence of the spin-forbidden molecular pathway in this reaction, never detected before, has been rationalized by invoking the occurrence of intersystem crossing between triplet and singlet manifolds of the C₃H₂ potential energy surfaces. The reaction CN(X²Σ⁺) + C₂H₂ has been found to lead to internally excited HCCCN (cyanoacetylene) + H. For all the reactions the dynamics have been discussed in the light of recent theoretical calculations on the relevant potential energy surfaces. Previous, lower resolution studies on C and CN reactions carried out using pulsed beams are noted. Finally, throughout the paper the relevance of these results to combustion chemistry is considered.