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By employing the exact diagonalization method,we investigate the low-energy behaviour of the dimerized spinless fermion chains with quasiperiodic modulation.It is found that for off-diagonal modulation,the energy gap with length N scales as exp(-cNω)with nonuniversal exponent ω if the dimerization is nonzero.However,for diagonal modulation,there may exist a critical dimerization δc beyond which the system exhibits a metal-insulator transition.