For the first time, accurate measurements of electron and positron fluxes in the energy range 0.2--10 GeV have been performed with the Alpha Magnetic Spectrometer (AMS) at altitudes of 370--390 km in the geographic latitude interval ¿51.7¿. We describe the observed under-cutoff lepton fluxes outside the region of the South Atlantic Anomaly. The separation in quasi-trapped, long-lifetime (O(10 s)), and albedo, short-lifetime (O(100 ms)), components is explained in terms of the drift shell populations observed by AMS. A significantly higher relative abundance of positrons with respect to electrons is seen in the quasi-trapped population. The flux maps as a function of the canonical adiabatic variables L, α0 are presented for the interval 0.95 < L < 3, 0¿ < α0 < 90¿ for electrons (E < 10 GeV) and positrons (E < 3 GeV). The results are compared to existing data at lower energies. The properties of the observed under-cutoff particles are also investigated in terms of their residence times and geographical origin.