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Propagation of electromagnetic waves in one-dimensional (1-D) stratified chiral structures is described by the 4×4 transfer-matrix method. The photonic bandgap (PBG) properties in 1-D periodical chiral media are investigated. The relation between PBG and chirality admittance has been anal-yzed. Under proper operating parameters, quite perfect multi-channel filtering properties can be obtained with the periodic structure. The photonic bandgap properties of one-dimensional layered periodical structures that include of double negative (DNG) medium, so-called backward-wave (BW) medium are investigated. The simulation results show that the width of the PBG in the structure composed of chiral medium and BW medium is larger then that composed of chiral medium and usual medium. Our analysis has shown that the usage of the negative material makes it possible to dramatically widen the band gap of one-dimensional photonic crystal.