[en] The stability of interstellar clouds against gravitational collapse and fragmentation in the presence of magnetic fields is investigated. A magnetic field can provide pressure support against collapse if it is strongly coupled to the neutral gas; this coupling is mediated by ion-neutral collisions in the gas. The time scale for the growth of perturbations in the gas is found to be a sensitive function of the fractional ion abundance of the gas. For a relatively large fractional ion abundance, corresponding to strong coupling, the collapse of the gas is retarded. Star formation is inhibited in dense clouds and the collapse time for diffuse clouds cn exceed the limit on their lifetime set by disruptive processes. For a small fractional ion abundance, the magnetic fields do not inhibit collapse and the distribution of the masses of collapsing fragments are likely to be quite different in regions of differing ion abundance. The solutions also predict the existence of large-scale density waves corresponding to two gravitational-magnetoacoustic modes. The conditions which best support these modes correspond to those found in the giant molecular clouds