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The electronic structures of the A1B(2)-type transition-metal diborides TMB(2) (TM=Sc, Ti, V, Cr, Mn, Y, ZT, Nb, Mo, Hf, Ta) have been calculated by using the self-consistent LMTO-ASA method. The binding mechanism is discussed and the rigid-band model is shown to provide a fairly good description of their electronic structures. The existence of a pseudogap in the total density of states is found to be a common feature of these compounds. The variation of the chemical stabilities of these diborides is analysed and we find that the trends can be understood in terms of the band-filling concept of the bonding states. The results are compared with other theoretical and experimental work.