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The finite-difference time-domain (FDTD) technique for simulating electromagnetic wave interaction with a dispersive chiral medium is extended to include the simulation of dispersive bianisotropic media. Due to anisotropy and frequency dispersion of such media, the constitutive parameters are represented by frequency-dependent tensors. The FDTD is formulated using the Z-transform method, a conventional approach for applying FDTD in frequency-dispersive media. Omega medium is considered as an example of bianisotropic media, the frequency-dependent tensors of which are based on analytical models. The extended FDTD method is used to determine the reflection and transmission coefficients of co- and cross-polarized electromagnetic waves from omega slabs, illuminated by normally incident plane waves. Three cases are simulated: 1) a slab of uniaxial omega medium with its optical axis parallel to the propagation vector; 2) a slab of rotated uniaxial omega medium with its optical axis not parallel to the propagation vector; and 3) a slab of biaxial omega medium. The results are validated by means of comparisons with analytical solutions.