There is strong evidence that both magnetic fields and ionized gas are widespread in our galaxy with powerful concentrations around stars and, in particular, the Sun. In such regions a localized disturbance will inevitably cause one or more of the different types of hydromagnetic waves. These are combined mechanical and electromagnetic waves, and the forces involved may far outweigh gravitational and other forces present. The electromagnetic forces, hitherto largely neglected, should be considered in many astrophysical problems. Most investigators of HM waves in gases have, for simplicity, assumed either perfect or isotropic conductivity which is seldom justified and completely hides the nature of the electromagnetic wave, In the present paper a general theory of weak HM waves in anisotropically conducting gas is developed. There are three such HM waves and for each the velocity, absorption, magnetic and electric fields, the Poynting vector and the gas velocity are found. The physical nature of some HM waves is discussed; these include, as limiting cases, radio waves in ionized gas and in vacuo. The effect of Maxwell's displacement current on HM waves is found to be generally small, but it does cause a space-charge electric wave to accompany the HM wave and this could have important consequences.