Three-dimensional observations of ion and electron velocity distributions with the Geotail spacecraft for three crossings of slow-mode shocks encountered in Earth's distant magnetotail are presented. Important findings from the observations are (1) the ion velocity distributions in the shock layer and the downstream region of the shocks are highly anisotropic because of the presence of multiple ion components in velocity space and (2) the pressure tensors in the downstream regions as determined from the measured velocity distributions can be diagonalized in magnetic field coordinates. A modification to the procedure for the identification of the slow-mode shocks is developed with an assumption of anisotropic, gyrotropic plasmas in order to take these observations into account. The predictions for the downstream plasma moments and magnetic fields from the modified procedure are in sufficient agreement with the measured parameters to provide considerably greater confidence in the identifications of the slow-mode shocks. The possibility that the boundaries are tangential discontinuities is eliminated with observations of upstream plasma mantle ions that penetrate the shock layer and enter the downstream hot plasmas. Also observed in the upstream ion velocity distributions is the presence of accelerated ions escaping from the downstream region which may play an important role in the dynamics of the slow-mode shock. Observations of the electron velocity distributions allow identification of the separatrix in Earth's magnetotail. The separatrix in the upstream region is identified with the first appearance of hot electrons streaming away from the shock. Flat-topped electron velocity distributions are found in the downstream region. ¿ American Geophysical Union 1996