Small-amplitude magnetohydrodynamic (MHD) waves are studied in a dilute collisionless plasma with an anisotropic pressure distribution. The parallel and perpendicular pressure are defined with the aid of two polytropic pressure laws. For specific values of the polytropic indices, previous results obtained with the usual Chew-Goldberger-Low (CGL) double-adiabatic (i) and double-isothermal (ii) models are recovered. The double-polytropic model can be considered as the counterpart of the single-polytropic model. Dispersion relations for the linear waves are derived and analyzed in the presence of pressure anisotropy. The weakly nonlinear dynamics is shown to be governed by the Benjamin-Ono equation. The results are discussed in the CGL and double-isothermal limits. ©2000 American Institute of Physics.