The title reaction was studied with various techniques in 1 M sulfuric acid, a usual medium for the oscillatory Belousov-Zhabotinsky (BZ) reaction. It was found to be a more complex process than the bromomalonic acid (BrMA)-BrO3- reaction studied previously in the first part of this work. Malonic acid (MA) can react with acidic bromate by two parallel mechanisms. The main aim of the present research was to determine the mechanisms, the rate laws, and the rate constants for these parallel channels. In one reaction channel the first molecular products are glyoxalic acid (GOA) and CO2 while in the other channel mesoxalic acid (MOA) is the first molecular intermediate, that is, no CO2 is formed in this step. To prove these two independent routes specific colorimetric techniques were developed to determine GOA and MOA selectively. The rate of the GOA channel was determined by following the rate of the carbon dioxide evolution characteristic for this reaction route. In this step, regarding it as an overall process, one MA is oxidized to GOA and CO2 and one BrO3- is reduced to HOBr, which forms BrMA with another MA. The initial rate of the GOA channel is a bilinear function of the initial MA and BrO3_ concentrations with a second-order rate constant k(GOA) = 2.4 x 10(-7) M-1 s(-1). The rate of the other channel was calculated from the rate of the BrO3-consumption measured in separate experiments, assuming that the measured depletion is a sum of two separate terms reflecting the consumptions due to the two independent channels. In the MOA channel one MA is oxidized to MOA and one BrO3_ is consumed while another MA is brominated as in the GOA channel. It was found that the initial rate of the MOA channel is also a bilinear function of the MA and BrO3-concentrations with a second-order rate constant k(MOA) = 2.46 x 10(-6) M-1 s(-1). Separate chemical mechanisms are suggested for both channels. In all of the various bromate-substrate reactions of these mechanisms oxygen atom transfer from the bromate to the substrate occurs generating bromous acid intermediate. This can be of high importance in BZ systems as bromous acid is the autocatalytic intermediate there. GOA and MOA also can be oxidized by acidic bromate but a study of these reactions will be published later.