For the first time accurate measurements of electron and positron fluxes in the energy range 0.2 \div 10 GeV have been performed with the Alpha Magnetic Spectrometer ( AMS ) at altitudes of 370 \div 390 km in the geographic latitude interval \pm 51.7 ^ { o } . We describe the observed under-cutoff lepton fluxes outside the region of the South Atlantic Anomaly ( SAA ) . 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 , \alpha _ { o } are presented for the interval 0.95 < L < 3 , 0 ^ { \mathrm { o } } < \alpha _ { o } < 90 ^ { \mathrm { o } } for electrons ( E < 10 GeV ) and positrons ( E < 3 GeV ) . The results are compared with 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 .