The wavelength and Einstein A coefficient are calculated for all rotation-vibration transitions of ^4^HeH^+^, ^3^HeH^+^, ^4^He^2^H^+^ and ^3^He^2^H^+^, giving a complete line list and the partition function for ^4^HeH^+^ and its isotopologues. This opacity is included in the calculation of the total opacity of low-metallicity stars and its effect is analysed for different conditions of temperature, density and hydrogen number fraction. For a low helium number fraction (as in the Sun), it is found that HeH^+^ has a visible but small effect for very low densities ({rho}<=10^-10^g/cm^3^), at temperatures around 3500K. However, for high helium number fraction, the effect of HeH^+^ becomes important for higher densities ({rho}<=10^-6^g/cm^3^), its effect being most important for a temperature around 3500K. Synthetic spectra for a variety of different conditions are presented.