Loss minima in two fluoride glass and chalcogenide glass fibres were calculated. The intrinsic losses are predicted to be 1 × 10−3 dB/km at 3.4 μm for BaF2-GdF3-ZrF4 glass fibre, 1 × 10−2 dB/km at 2.7 μm for BaF2-CaF2-YF3-AlF3 glass fibre and 1 × 10−2 dB/km at 4.5 μm for GeS3 glass fibre.