Boron layers (grown by thermal decomposition of B10H14) on the (0001) Si- and (0001BAR) C-terminated surfaces of alpha-SiC have been studied using Auger and electron energy-loss spectroscopies and low-energy electron diffraction. Adsorption of O2 on the clean and B-adsorbed surfaces was also studied. Cleaning the (0001) surface by annealing in a flux of Si vapor gives a (3 x 3) structure which converts to (square-root 3 x square-root 3)R30-degrees upon further annealing in vacuum. The (3 x 3) consists of an ordered layer of Si chemisorbed on the Si termination layer, while the (square-root 3 x square-root 3)R30-degrees involves an ordered arrangement of Si vacanies. A (1 x 1) structure is observed for the clean C-face. Adsorption of B on the (3 x 3) Si-face eliminates the reconstruction, and further annealing produces a complicated superstructure. Stronger interaction occurs on the (square-root 3 x square-root 3)R30-degrees Si-face leading to an incommensurately ordered (1 x 1) layer loosely termed ''Si boride'' due to the substantial changes in SiL2,3VV and BKLL Auger lineshapes. On the C-face, a disordered B layer forms. On B-free surfaces, room-temperature chemisorption of O2 is slower on the (1 x 1) C-face than on the (3 x 3) Si-face, but the rates of O uptake become comparable with increasing coverage as chemisorption gives way to oxidation. For the (square-root 3 x square-root 3)R30-degrees Si-face, chemisorption is rapid, but oxidation very slow. For all three surfaces, adsorbed B suppresses chemisorption of O2 but has little or no effect on oxidation.