In this paper we consider the problem of second sound propagation in a quasiparticle system which has a high level of anisotropy. The main aim of the research is to derive an exact expression for the second sound velocity in such a system, which is valid for any value of the velocity of the quasiparticle system relative to the superfluid. We can then consider the propagation of thermal perturbations in anisotropic systems of both phonons and rotons in He(II). We compare the results with previous