The direct product ofpsingle parity-check codes of block lengthsn_1,n_2, cdots ,n_pis a cyclic code of block lengthn_1 times n_2 times cdots times n_pwith(n_1 - 1) times (n_2 - 1) times cdots times (n_p - 1)information symbols per block, if the integersn_1,n_2 cdots ,n_pare relatively prime in pairs. A lower bound for the single-burst-correction (SBC) capability of these codes is obtained. Then, a detailed analysis is made forp = 3, and it is shown that the codes can correct one long burst or two short bursts of errors. A lower bound for the double-burst-correction (DBC) capability is derived, and a simple decoding algorithm is obtained. The generalization to correcting an arbitrary number of bursts is discussed.