The kinetics and mechanism of the title heterogeneous halogen exchange reactions of potential atmospheric importance have been studied under molecular flow conditions in a FEP Teflon-coated Knudsen flow reactor on HX (X = Cl, Br, I) - doped ice condensed from the vapor phase under conditions of several formal monolayers of HX coverage at approximately 200 K. In addition, the halogen exchange reactions involving the expected primary reaction products BrCl, ICl and IBr of the above mixed anhydrides with HX-doped ice have been studied at 200 K as well. The uptake coefficient γ for the heterogeneous reaction ClONO2 + HBr on ice is 0.56±0.11 and Cl2 and Br2 are formed in yields of 100% and 66 to 80%, respectively, in the range 180 to 200 K. The γ value for the reaction ClONO2 + HI on ice is 0.30±0.02 at 200 K with Cl2 being the main product appearing after an induction time. The primary product ICl is formed at the same time as Cl2 whereas HOCl appears at a later time under conditions of waning HI supply. The γ value for the reaction BrONO2 + HI on ice is 0.40±0.02 at 200 K with Br2 being the main product observed after a short delay. The primary product IBr is observed without delay, whereas HOBr is observed at a later time once HBr has reacted. The mechanism of the reactions of the interhalogens BrCl, ICl and IBr with HX on ice at 200 K involves the formation of trihalide ions at the ice interface which is consistent with the observed significant negative temperature dependence for the reaction ICl + HBr on ice in the range 180 to 205 K as well as for the reaction BrCl + HBr between 190 and 200 K. The uptake coefficient γ for each of the interhalogens increases from ice to HI-doped ice in the order of increasing molecular weight of HX with the exception of ICl, whose g attains a limiting value of γ = 0.32±0.05. A halogen exchange reaction on ice has been observed in cases where the most stable hydrohalic acid could be formed: HCl > HBr > HI. A propensity for the formation of the homonuclear halogen molecule in the reactions of halogen nitrates with HX-doped ice has been explained by the occurrence of fast secondary reactions of the primary interhalogen product at the HX/ice interface.