The magnetosheath plasma is usually neither isotropic nor adiabatic. This paper contains an attempt to describe its thermodynamic properties in terms of two polytropic laws, p⊥/&rgr;B&ggr;⊥-1=C⊥ and p∥B&ggr;∥-1/&rgr;&ggr;∥=C∥, such that for &ggr;⊥=2, &ggr;∥=3 the usual Chew-Goldberger-Low double-adiabatic expressions are recovered and for &ggr;⊥=1, &ggr;∥=1 double-isothermal conditions are obtained. Using data from the AMPTE/IRM spacecraft, we show that the subsolar magnetosheath plasma may be better described by the double-polytropic laws than by the mirror instability threshold, in particular in the low beta region near the magnetopause. The inferred polytropic exponents vary from event to event but are typically in the ranges of &ggr;⊥=0.94¿0.10 and &ggr;∥=1.14¿0.13 for the 29 cases we have examined. ¿ American Geophysical Union 1993