The polarization in elastic proton-proton and proton-neutron scattering has been measured at an incident kinetic energy of 1.03 GeV. The proton-proton data have a significantly higher precision than previously obtained in this energy range and extend into the Coulomb interference region. The proton-neutron measurement is the first in this energy region. The results are compared with existing nucleon-nucleon phase shifts solutions. NUCLEAR REACTIONS Polarization in pp and pn scattering, GeV energies, measurement.