The aim of this study is to improve understanding of the tropospheric oxidation of ethyne (acetylene, C2H2) and but-2-yne, which takes place in the presence of HO and O-2. The details of the potential energy hypersurface have been discussed in a previous article [Maranzana et al., J. Phys. Client. A 2008, 112, XXXX]. For both molecules, the initial addition of HO radical to the triple bond is followed by addition of O-2 to form peroxyl radicals. In both reaction systems, the peroxyl radicals take two isomeric forms, E1 and E2 for ethyne and e1 and e2 for but-2-yne. Energy transfer parameters (alpha = 250 cm(-1)) for the ethyne system were obtained by simulating laboratory data for N-2 buffer gas, where O-2 was not present. In simulations of C2H2 + HO when O-2 is present, E1 reacts completely and E2 reacts almost completely, before thermalization. Radical El produces formic acid (similar to 44%) and E2 gives glyoxal (similar to 53%), in quite good agreement with experiments. For but-2-yne, pressure-dependent laboratory data are too scarce to obtain energy transfer parameters directly, so simulations were carried out for a range of values: alpha = 200-900 cm(-1). Excellent agreement with the available experimental yields at atmospheric pressure was obtained with (X = 900 cm(-1). Two reaction channels are responsible for acetic acid formation, but one is clearly dominant. Biacetyl is produced by reactions of e1 and, to a minor extent, e2. The peroxyl radical e2 leads to less than 8% of all products. Vinoxyl radical (which has been reported in experiments involving C2H2 + HO) and products of its reactions are predicted to be negligible under atmospheric conditions.