Polyynic structures in fuel-rich low-pressure flames are observed using VUV photoionization molecular-beam mass spectrometry. High-level ab initio calculations of ionization energies for C2nH2 (n=1-5) and partially hydrogenated CnH4 (n=7-8) polyynes are compared with photoionization efficiency measurements in flames fuelled by allene, propyne, and cyclopentene. C2nH2 (n=1-5) intermediates are unambiguously identified, while HC[triple bond, length as m-dash]C-C[triple bond, length as m-dash]C-CH=C=CH2, HC[triple bond, length as m-dash]C-C[triple bond, length as m-dash]C-C[triple bond, length as m-dash]C-CH=CH2 (vinyltriacetylene) and HC[triple bond, length as m-dash]C-C[triple bond, length as m-dash]C-CH[double bond, length as m-dash]CH-C[triple bond, length as m-dash]CH are likely to contribute to the C7H4 and C8H4 signals. Mole fraction profiles as a function of distance from the burner are presented. C7H4 and C8H4 isomers are likely to be formed by reactions of C2H and C4H radicals but other plausible formation pathways are also discussed. Heats of formation and ionization energies of several combustion intermediates have been determined for the first time.