A model is developed for small-amplitude waves propagating in a magnetically structured plasma with anisotropic pressures. Closure of the magnetohydrodynamic (MHD) equations is provided by apairofpolytropiclaws, p ⊥ρ-1B1γ⊥ = C ⊥ and p∥ρ-γ∥B γ∥-1 = C∥, such that for γ⊥=2, γ∥=3 the usual Chew-Goldberger-Low double-adiabatic expressions are recovered and for γ⊥ = 1, γ∥=1 double-isothermal conditions are obtained [L.-N. Hau and B. U. Ö. Sonnerup, Geophys. Res, Lett. 20, 1763 (1993)]. The wave equation represents the counterpart of that obtained for the isotropic plasma using the single energy equation, pρ-γ= C. Two applications are considered: the occurrence of surface waves on a magnetic interface and the field-line resonance.