There are four low-frequency modes which may propagate in a high-beta nearly bi-Maxwellian plasma. These are the magnetosonic, Alfv¿n, ion acoustic, and mirror modes. This manuscript defines a procedure based on linear Vlasov theory for the unique identification of these modes by use of transport ratios, dimensionless ratios of the fluctuating field and plasma quantities. A single parameter, the mode deviation, is defined which characterizes the difference between the theoretical transport ratios of a particular mode and the observed ratios. The mode deviation is calculated using the plasma and magnetic field data gathered by the Active Magnetospheric Particle Tracer Explorers/Ion Release Module spacecraft to identify the modes observed in the terrestrial magnetosheath near the magnetopause. As well as determining the mode which best describes the observed fluctuations, it gives us a measure of whether or not the resulting identification is unique. Using 17 time periods temporally close to a magnetopause crossing, and confining our study to the frequency range from 0.01 to 0.04 Hz, we find that the only clearly identified mode in this frequency range is the mirror mode. Most commonly, the quasi-perpendicular mirror mode (with wave vector k roughly perpendicular to the background magneticc field B0) is observed. In two events the quasi-parallel mirror mode (k ∥ B0) was identified. ¿ American Geophysical Union 1995