| 摘 要： | In1], Liu Shaoxue investigated the structure of the additive categories. Nowwe give consideration to the weakly additive category A=∪_αA_β, in which thering _αA_α need not contains unity element. In this paper, we construct radicals of weakly additive categories using twomethods, one by module-theoretic characterization and the other by generalizationof radical properties of rings. In consequence, we get the known results of theradicals of additive categories. We also define some new radicals by means of theradical properties of rings. This is the application of the radical-theoretic method
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