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The acoustic birefringence in a highly birefringent (Hi-Bi) two-mode optical fiber is measured and shown to be about 0.8%. The birefringence is primarily caused by a cladding ellipticity in excess of 1%. The effect of the softer stress-inducing elements is small in comparison. The effects of misalignment of the acoustic and optical axes is studied in detail using both continuous-wave and pulsed acoustooptic interaction. In the Hi-Bi fiber, the misalignment is approximately 20°. The acoustic birefringence and misalignment have a profound effect on the spectral characteristic of tunable acoustooptic notch- and passband filters, giving rise to double spectral peaks. The birefringence is not specific to Hi-Bi fibers. The same effect is demonstrated in a birefringent elliptic core fiber, and it should be expected also in standard telecom single-mode fibers. In tunable acoustooptic notch filters based on coupling to cladding modes in standard telecom fibers with ellipticity of the order of 1% the acoustic birefringence may cause double absorption peaks separated by more than 4 nm. It is also shown that acoustic birefringence provides guiding of the spatial orientation of the acoustic flexural waves, even if the fiber is twisted. This guiding effect eases the construction of acoustooptic components with long interaction length.