In this work, we generalise linear magnetohydrodynamic (MHD) stability theory to include equilibrium pressure anisotropy in the uid part of the analysis. A novel `single-adiabatic' (SA) uid closure is presented which is complementary to the usual `double-adiabatic' (CGL) model and has the advantage of naturally reproducing exactly the MHD spectrum in the isotropic limit. As with MHD and CGL, the SA model neglects the anisotropic perturbed pressure and thus loses non-local fast-particle stabilisation present in the kinetic approach. Another interesting aspect of this new approach is that the stabilising terms appear naturally as separate viscous corrections leaving the isotropic SA closure unchanged. After verifying the self-consistency of the SA model, we re- derive the projected linear MHD set of equations required for stability analysis of tokamaks in the MISHKA code. The cylindrical wave equation is derived analytically as done previously in the spectral theory of MHD and clear predictions are made for the modi cation to fast-magnetosonic and slow ion sound speeds due to equilibrium anisotropy.