An unambiguous determination of the wave modes observed in plasma turbulence requires the determination of the dispersion characteristics of the wave. The method adopted for the determination of the wave dispersion relation is based upon the study of the phase difference of the waves at two closely separated spacecraft [Balikhin and Gedalin, 1993>. It is applied to observations of waves in the magnetosheath magnetic field made by AMPTE UKS and AMPTE IRM. We show that the observed waves are propagating in the sunward direction but are convected toward the magnetopause by the plasma flow. As a result, the observed waves are quasi-standing in the flow. These waves have been previously identified as either slow or mirror modes depending the procedure adopted for their analysis. They may also be an experimental observation of the mirror and slow (MIAOW) waves identified near the magnetopause boundary in the hybrid simulations of Omidi and Winske [1995>. The observed waves possess short wavelengths (&lgr;) such that RBi/&lgr;≈1 (where RBi is the ion Larmor radius). Thus they may only be studied analytically within the framework of the kinetic approximation. Both the nonlinear amplitudes and possibly the strong underlying inhomogeneity are responsible for the significant differences between the properties of the observed modes and those resulting from linear homogeneous kinetic theory. ¿ 2001 American Geophysical Union