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We present octave-wide bandpass filters in the terahertz (THz) region based on bilayer-metamaterial (BLMM) structures. The passband region has a super-Gaussian shape with a maximum transmittance approaching 70% and a typical stopband rejection of 20 dB. The design is based on a metasurface consisting of a metallic square-hole array deposited on a transparent polymer, which is stacked on top of an identical metasurface with a subwavelength separation. The superimposed metasurface structures were designed using finite-difference time-domain (FDTD) simulations and fabricated using a photolithography process. Experimental characterization of these structures between 0.3 and 5.8 THz is performed with a time-domain THz spectroscopy system. Good agreement between experiment and simulation results is observed. We also demonstrated that two superimposed BLMM (2BLMM) devices increase the steepness of the roll-offs to more than 85 dB/octave and enable a superior stopband rejection approaching 40 dB while the maximum transmittance remains above 65%. This work paves the way toward new THz applications, including the detection of THz pulses centered at specific frequencies, and an enhanced time-resolved detection sensitivity toward molecular vibrations that are noise dominated by a strong, off-resonant, driving field.