Summary: The authors study the tensor modes of perturbations of a two-fluid model in general relativity, where one of the fluids has the equation of state \(p=-\rho/3\) (a variable cosmological constant, a cosmic string fluid, a texture) or \(p=-\rho\) (a cosmological constant), while the other is ordinary matter (radiation, stiff matter, incoherent matter). In case (a), with the stringlike fluid, the spatial section is compact but the scale factor evolves in a way similar to that in an open Universe with positive pressure, providing alternative solutions for the age and horizon problems. The study of gravitational waves is extended to all values of the effective curvature \(k_{eff} =k-{8\over 3} \pi G\rho_{0s}\), that is, positive, negative or zero, \(k\) being the curvature of the spacelike section. In case (b), with a cosmological constant, we restrict ourselves to a flat spatial section. The behaviour of gravitational waves has, in each case, particular features, that can be reflected in the anisotropy spectrum of the cosmic microwave background radiation. They also make some considerations on these exotic fluids as candidates for dark matter models.